A federal judge has questioned the city’s record of investigating allegations that Boston police officers used excessive force, issuing a ruling that keeps alive a lawsuit claiming the city has allowed police misconduct to go unpunished.

The judge’s criticism came in a lawsuit brought by a Boston man, Nicholas Cox, who said he was beaten by two police officers who thought they saw him participating in a drug deal near Orchard Park in 2010. Both officers have a history of complaints against them, though Boston police records show in some cases the city did not investigate seemingly obvious misconduct.

“Put simply, a very large amount of smoke could reasonably compel the inference that there must be at least a small amount of fire,’’ US District Judge F. Dennis Saylor IV said in a ruling unsealed March 11 that allows Cox’s suit to move forward. “This is such a case.’’

The judge’s ruling comes as police departments across the country are facing criticism for misconduct and shootings of unarmed individuals.

Boston police have generally won praise from civic leaders. However, a Globe survey earlier this year found that a dozen officers faced 20 or more complaints over the past 20 years, and that internal affairs investigations sometimes languished for years.

The judge noted in his ruling that Boston police internal affairs investigations rarely sustain complaints: Of the 698 complaints alleging improper use of force from 2001 to 2011, only 18 were sustained, and many remained open for years without resolution.

Saylor’s ruling allows the lawsuit to continue so that the claims of police abuse could eventually be heard by a jury. The judge rejected the city’s request to remove it from the lawsuit as a defendant.

“A reasonable jury could . . . conclude that the city did not take appropriate action in response, and indeed on some occasions did not even conduct a meaningful investigation,’’ the judge said.

The mayor’s office and the Boston Police Department declined to comment on Cox’s suit because it is pending. The unions representing the officers named in the lawsuit did not return calls seeking comment.

The ruling supported one of Cox’s key claims: that the City of Boston could be held liable for its failure to supervise and discipline the two officers, which, as Cox’s lawyers had alleged, “created an atmosphere in which the officers believed they could violate an arrestee’s civil rights with impunity.’’

“The decision points to [the] fact that when individual police officers repeatedly engage excessive force, the internal structures of the police departments which allow this behavior to continue should be called into question,’’ said Jessica Hedges, of Hedges & Tumposky, one of the lawyers involved in the suit.

“The evidence that we have uncovered in this lawsuit suggests that the BPD and its internal affairs functions are turning a blind eye to officers who repeatedly engage in violence in our community. Such institutional failures thereby create a culture in police departments where the use of excessive force is sadly predictable.’’

Each of the two officers — Sergeant Detective Paul Murphy, who now works in the department’s special investigations unit, and Officer Sean Flaherty, a member of the drug control unit — has a lengthy history of misconduct allegations that were never acted on by internal affairs investigators, the judge found.

A third officer, former detective Brian Smigielski, allegedly falsified police reports of the incident with Cox, according to the lawsuit. Smigielski resigned from the force last year. He was sentenced in federal court in January to a year of probation for lying to FBI agents about a separate investigation.

The ruling echoes the Globe’s review of complaints filed against police officers.

The Globe found that Boston spent more than $41 million to resolve thousands of legal claims and lawsuits against the police department over the past decade. Most of the money was spent to settle cases that alleged wrongful convictions or police misconduct.

Smigielski was the subject of five complaints between 2004 and 2009, according to Boston Police Department records; none was sustained.

Flaherty received 10 complaints between 2003 and 2013, including five alleging inappropriate use of force, according to the department. One complaint, in 2006, was sustained.

Murphy was the subject of 16 complaints between 1993 and 2013, including nine alleging inappropriate use of force. Only one complaint was sustained — one filed by a member of the department in 1999.

In one of the complaints cited in Saylor’s ruling, Murphy was accused in 2009 of choking and punching a man who was taken to the emergency room; Flaherty also was present during that incident.

Also, in 2011, Murphy arrested a man he knew from his work in South Boston, and Murphy can be heard in an audio recording threatening to beat the man “within an inch of [the man’s] life.’’ The tape was forwarded by state prosecutors to police investigators, who never questioned Murphy about it, according to Saylor’s ruling. That same month, he was transferred out of the drug control unit.

Murphy has also been named in five civil lawsuits, three of which the city settled and one that is still pending. A fifth was resolved in his favor. He was never disciplined for any of those incidents, according to the ruling.

Murphy was also accused in 2002 of indecently assaulting a young girl, though internal affairs investigators never questioned him about the incident, according to the ruling. In 2007, he was accused of choking a 14-year-old girl, though that allegation was not substantiated.

“It appears that the most severe discipline Murphy has ever received for any incident was an oral reprimand,’’ the judge found.

In his ruling, Saylor noted that police officers are likely to be accused of misconduct, sometimes erroneously, and he acknowledged that police officers, who have difficult and sometimes dangerous jobs, can at times commit forgivable errors. But he questioned whether the officers’ history of allegations of abuse that were outlined in the ruling and the city’s failure to sustain the allegations were indicative of more systemic problems.

“A supervisor could reasonably infer that when an individual officer accumulates a high or disproportionate number of complaints of excessive force or related misconduct, some further action . . . is warranted,’’ the judge said, adding that, “Nicholas Cox is by no means the first person to allege that Murphy choked him, punched him, or otherwise used excessive force.’’

The judge added, “Given that evidence, a reasonable jury could conclude that the city was on notice as to the possible propensity of Murphy, or Murphy and Flaherty together, to use excessive force during arrests.’’

Representatives of local civil rights groups lauded the judge’s decision.

“What is troubling is the officers being sued here have really bad histories,’’ said Ivan Espinoza-Madrigal, executive director of the Lawyers Committee for Civil Rights and Economic Justice. “It shows there is misconduct taking place, excessive force being used, and the city has not disciplined, has not properly investigated these incidents, and that’s concerning to the court.’’

Boston civil rights attorney Howard Friedman said most Boston police officers end their careers with no complaints or one complaint. The fact that the officers named in the suit have such lengthy complaint histories, he said, is disturbing.

“The department is not doing all that it can; it’s not even trying,’’ said Friedman. “Four complaints of choking and punching should indicate that something is wrong. What message does that send?’’

Milton J. Valencia can be reached at milton.valencia @globe.com. Jan Ransom can be reached at jan.ransom @globe.com.