HARTFORD — Leaders of the Connecticut NAACP have met with State Police officials over the past several months to discuss their concerns about what they call a longstanding lack of diversity among troopers and their supervisors.

The talks were prompted earlier this year by a photo of a largely white graduating class at the State Police Academy, said Tamara Lanier, criminal justice chairwoman of the state NAACP chapter.

‘‘We’ve gotten a number of complaints,’’ Lanier said. ‘‘There’s a concern that the process . . . . is not in favor of diversity, is not promoting equal access to the opportunities.’’

Nearly 4,500 blacks and 4,200 Hispanics have applied to be Connecticut state troopers since 2004, but only 28 African-Americans and 38 Hispanics graduated from the academy in that time frame, according to information obtained through public records requests. Blacks and Hispanics account for a third of the applicants, but only 11 percent of academy graduates. Over the same period, about 15,000 whites applied to be troopers and 527 graduated from the academy.

‘‘It’s unacceptable,’’ said Scot X. Esdaile, president of the state NAACP. ‘‘There are a lot of concerns now about diversity in law enforcement. We’re tired of hearing excuses. They can do better. The needle has not moved at all.’’

Police in several Connecticut cities and towns also have come under scrutiny from the NAACP and other groups, after state reports that said police were stopping black and Hispanic drivers and firing stun guns at minorities at disproportionate rates.