FRAMINGHAM — In another black eye for the scandal-ridden Massachusetts State Police, 20 active troopers face potential sanctions for the apparent theft of overtime pay, with the most egregious alleged offenders putting in for as many as 100 no-show shifts, officials said Tuesday.

In a state agency where 245 troopers — about 12 percent of the force — made more than $200,000 last year, an internal audit of Troop E, a division that covers the Massachusetts Turnpike, found “apparent discrepancies between overtime paid and actual patrols worked,’’ State Police Colonel Kerry A. Gilpin, superintendent of the force, said at a morning news conference.

Nineteen troopers face internal duty status hearings in the coming days to determine whether they’ll be suspended, Gilpin said. Another trooper who was already suspended for another matter and a retiree are also being investigated.

Gilpin said that she couldn’t put a dollar figure on the amount of disputed overtime, but that the number of questionable overtime shifts per trooper ranged from one to “as high as 100.’’

State Police officials said they have reported their findings, which stemmed from an investigation launched last fall, to Attorney General Maura Healey’s office for review and potential prosecution.

Coming on the heels of several other high-profile controversies in recent months, news of the purported overtime scheme quickly stirred outrage.

Governor Charlie Baker, who appointed Gilpin to head the agency last November, said the superintendent “made a pretty clear statement that this sort of activity and this sort of behavior is not going to be tolerated.’’

Baker said that overall the State Police are “a strong, good, well-trained unit.’’

“But clearly there’s some people here who broke the rules, allegedly, and got way beyond the bounds of what anyone would consider to be appropriate behavior,’’ Baker said. “And for those who are found to have committed what’s been alleged, they should face the music.’’

The department’s previous superintendent, Richard McKeon, and his deputy, Francis Hughes, retired in November after revelations that McKeon had ordered an arrest report changed to remove embarrassing information about the daughter of Judge Timothy Bibaud. A lawyer for McKeon has said he ordered the deletions to remove unnecessary information.

Baker and Healey have each announced investigations into the handling of the police reports.

Two more high-ranking officials linked to the redactions – Lieutenant Colonel Daniel Risteen and Major Susan Anderson — retired suddenly in February. Their retirements came a day after the Globe reported that Trooper Leigha Genduso had been hired despite having been a coconspirator in a 2007 drug case and having avoided charges by testifying. Genduso, whom multiple sources said was Risteen’s former girlfriend, was suspended after the disclosure.

On Tuesday, the union that represents troopers, the State Police Association of Massachusetts, said it does not condone any actions that may have violated the public’s trust.

“The department has been in turmoil over the last several months,’’ Dana Pullman, president of the union, said in a statement. “We believe the customs and culture that was allowed to flourish under the previous state police leadership has compromised the public’s perception and calls into question the integrity of the hard-working men and women of the Massachusetts State Police. Colonel Gilpin has been given the unenviable task of dealing with a myriad of untenable issues.’’

The Globe reported earlier this month that many state troopers pad their salaries by working long overtime shifts or extra details. The median pay for a state trooper last year was just over $145,000.

Needham attorney Timothy M. Burke, who represents a large number of State Police superior officers, declined to identify the lieutenants facing possible disciplinary action, but said he believes they are under scrutiny for their supervision of troopers assigned to overtime details.

“My understanding based on information available at this time is the department is evaluating whether there was adequate supervision by those commissioned officers facing duty status hearings as opposed to the nonperformance of details,’’ Burke said.

Gilpin did not identify the troopers, sergeants, and lieutenants under investigation.

“Depending on the outcome of the [upcoming duty status] hearings, these members face a potential change in their duty status, up to and including suspension without pay, while further investigation into the apparent payment discrepancies is conducted,’’ Gilpin said.

Gilpin said her predecessor, McKeon, launched the audit of overtime shifts on Troop E last year after a discrepancy came to light between overtime hours filed and actual shifts worked. The audit reviewed overtime payments for traffic enforcement patrols on the Turnpike, known as Accident and Injury Reduction Effort, or AIRE, patrols, she said. The audit covered 2016, but State Police are extending their review of overtime use to additional years, Gilpin said.

Healey’s office confirmed Tuesday that prosecutors have received the audit and will investigate the findings.

The accusation that more than 20 troopers logged overtime they didn’t work would seem to warrant criminal charges, said David Rossman, a former prosecutor in Middlesex County who now directs criminal law clinical programs at Boston University.

“Short answer is: Yes, it does describe a crime because they stole money from the state by misrepresenting their entitlement to the money,’’ Rossman said. Whether prosecutors can bring a successful case is an open question, he said.

“It appears to be a widespread problem that requires some definitive response that demonstrates to the public that we don’t tolerate employees lying and stealing from the treasury,’’ he said. “But if there’s some common theme, like it went through one particular lieutenant, then it becomes a much easier case (to prove). If it’s just 20 individual troopers obviously doing the same thing and talking with each other about it, it becomes harder.’’

State Representative Timothy R. Whelan, a former state trooper and a Brewster Republican, said the move to hand the investigation to Healey struck him as an attempt to avoid criticism that an internal investigation would be compromised.

“It’s about restoring that confidence,’’ said Whelan. He applauded Gilpin as a “straight shooter’’ he has known since she was a rank-and-file trooper. Whelan said the accumulation of scandals at the department points to systemic problems that predate her.

State Police spokesman David Procopio said the agency’s internal affairs department initially began investigating one trooper for multiple issues, including overtime discrepancies, and WCVB-TV then made inquiries about additional troopers. The news station reported on the questionable overtime practices in October.

Some of the troopers now facing duty status hearings were initially reported by the news station, while numerous others were pegged by investigators, Procopio said.

One state trooper, Eric Chin, has been suspended without pay since last April amid allegations that he was paid for overtime shifts that he didn’t work.

On Monday, Chin filed a complaint with the Massachusetts Commission Against Discrimination, claiming he was unfairly disciplined because he is Asian, according to his lawyer.

The complaint alleges that when Chin was suspended, State Police allowed at least six lieutenants and one trooper who were accused of similar overtime violations — and are all white — to be reassigned rather than suspended.

“Since the initial investigation, it has been discovered at least another 20+ troopers were engaging in similar activities and it appears to be the accepted practice within Troop E,’’ the complaint stated. “No other trooper or supervisor have been disciplined as of this complaint.’’

After Gilpin announced Tuesday that more troopers may face discipline, Chin’s lawyer said it was common practice for troopers to sign up for overtime shifts to conduct traffic enforcement patrols, then collect the extra pay even when their supervisors canceled the patrols because of weather.

“It’s our intent to show this was a widespread and accepted practice approved by the command staff,’’ said Douglas I. Louison, who represents Chin. “Trooper Chin did certainly not instigate or initiate this practice, and he was not alone in knowing how it was managed.’’

Gilpin said State Police ended the AIRE patrols last year and took measures to strengthen “accountability and oversight of remaining overtime shifts.’’

“To date, we have no information to suggest these discrepancies are wider in scope than what we have announced today, but we are committed to full accountability throughout the entire department and thus will do our due diligence in that regard,’’ Gilpin said.

Joshua Miller of the Globe staff and Globe correspondents Matt Stout and Elise Takahama contributed to this report.