State officials are investigating whether a group of Boston firefighters cheated during a civil service promotional exam in November, taking turns going to the men's room, tapping out answers on their cellphones, and sending text messages to their colleagues in the testing room.

The state Human Resources Division confirmed that it received an anonymous complaint about cheating during a lieutenant exam taken by 186 firefighters and felt it credible enough to launch an investigation. If proved true, the allegations could force the agency to scrap the test results and administer a new test.

The division did not disclose details of the complaint. But the alleged scheme, said to have been carried out on Nov. 17, was described by three public officials who spoke on the condition of anonymity because of the sensitivity of the probe. The number of cheaters appears to have been fewer than 10, the officials said.

It would be the second time in less than a year that cheating was found to have occurred on a promotional exam for Boston public safety employees.

Results from a Boston Police Department detectives' exam had to be thrown out in July after officials discovered a number of test-takers had learned in advance that the test did not include questions from part of the study materials. That test was administered by a private contractor hired by the Police Department.

The latest allegations raise questions about the security of civil service examinations.

The Human Resources Division handles civil service testing for police and fire departments across the state, including entrance exams and promotional tests designed to qualify police officers and firefighters as chiefs, captains, and lieutenants. The division also administers tests for guards at state prisons.

"We take the integrity of the test, and any allegations of wrongdoing in this process, very seriously and will take appropriate action if the investigation finds misconduct." Sally McNeely, director of the division's Organizational Development Group, said in a statement Friday.

McNeely said there are strict protocols for security during testing, including a written notice to applicants well before the test that no cellphones or electronic devices are allowed.

If the firefighters ignore that instruction and bring cellphones or devices anyway, they are given new instructions.

"They are also told by the room proctor, during the test instructions, that, if they did bring communication devices into the test site, they must immediately turn them off and place them on the floor underneath their assigned seats and must not retrieve them until they are dismissed from the exam," McNeely said in the statement.

Within days of the test at the Atlantic Middle School in Quincy, rumors began to swirl in the Boston Fire Department about the group of test-takers exchanging answers via text messages.

An alleged eyewitness penned the anonymous complaint to the state, listing the names of those allegedly involved and outlining the scheme, according to two public officials who spoke on the condition of anonymity.

State officials said they received the complaint Dec. 14 and could not say how long the investigation will take.

Fire officials declined to comment on the allegations, referring questions to test administrators.

"The state gives the test so we would not have any comment," said Steve MacDonald, department spokesman. He also would not say whether disciplinary measures would be taken if firefighters are found to have cheated.

The firefighter lieutenants' exam is highly competitive, with more than 100 applicants testing for typically 20 or so openings each year for the position in the Boston Fire Department. Lieutenants made an average of $81,640 in 2006, about $16,600 more than rank-and-file firefighters, department payroll records show.

According to a job description posted online, lieutenants are responsible for evaluating fire scenes and determining tactics and strategy, noting factors such as structure type, wind conditions, temperature, and water availability.

To earn a promotion to lieutenant, applicants must pass the rigorous written exam administered by the state.

The reading list for the test includes seven textbooks, 50 sections of the Massachusetts general laws, and four Boston Fire Department handbooks. The test covers, among other subjects, chemistry and physics, hydraulics, ladder and pump operations, building design, and major- emergency response tactics.

The Human Resources Division administers the test once every other year, usually in November.

The civil service testing system, which dates to the 1880s, was the subject of widespread scandal in the 1980s, when several police officers were indicted on charges of stealing copies of tests and selling them for $3,000 each. The exam scam, as it was called, spurred calls for the state to turn over responsibility for the testing to an outside company, but it hasn't.

As early as 1978, the results of an entrance exam for firefighters were thrown out after the Globe Spotlight team reported that the test had been sold to some applicants out of a Revere bar.

One government watchdog group said Friday that if cheating is proven in the latest case, security for all civil service exams should be reviewed. "Clearly this seems to be a message that there needs to be a revision of civil service procedures in administering the tests and protecting the integrity of the tests," said Samuel R. Tyler, president of the Boston Municipal Research Bureau.

"The results should be based on the work preparing for the test and not based on other means," he said.