“One thing I’ll tell you about my son,’’ Menino said. “He doesn’t come back to me and say, ‘Dad, this guy is a real SOB,’ or ‘He’s a guy who doesn’t do his job.’ ’’

In an interview, the mayor said he had no role in the decision to demote Perkins, and said he and his son never talk about department business. The younger Menino has been on the force since 1994, and assigned to the intelligence center since July 2006.

The younger Menino is widely regarded by his colleagues in the department as a detective who, while working some coveted assignments, is a hard-charging officer who relishes the often thankless work of the street. There has never been any indication that he has looked to his father for help.

The demotion of Perkins and the outcry it provoked inside the Boston Police Department underscore the tenuous line that Mayor Menino walks while having a son on the city payroll, working in a high-visibility department in which rank-and-file members scrutinize every personnel maneuver in search of political influence.

In the months before Perkins’s demotion, Menino’s overtime, which had been among the highest in the Intelligence Center, and use of unmarked police cruisers had fallen off amid a department-wide budget crackdown that Perkins implemented inside the unit. A police official close to Davis acknowledged that Perkins asked the commissioner during their private meeting whether his dealings with Detective Menino played a role in his firing. Davis did not respond to Perkins, the official said.

While all police commanders serve at the discretion of the commissioner, Davis’s actions, taken on May 29, still have some members of the department hypothesizing that the trigger was the relationship between Perkins and one of the detectives he supervised, Detective Thomas M. Menino Jr., the mayor’s son.

Asked recently why he demoted Perkins from a command position he had appointed him to, Davis declined to offer any reasons, saying he doesn’t comment on transfers he makes inside the department.

Boston Police Commissioner Edward F. Davis removed Earl O. Perkins as commander of the Boston Regional Intelligence Center, reduced his rank from deputy superintendent to sergeant detective, and cut his salary by about $35,000. Davis offered no public explanation at the time, and department officials with direct knowledge said he gave Perkins no reasons when he summoned him in for the demotion.

A senior Boston police commander was recently demoted as head of the department’s elite and well-regarded intelligence-gathering unit, a surprise decision that has sparked questions among the ranks over whether City Hall was exerting an unusual level of influence over the management of the police department.

Menino said in the Globe interview that he reviews all the police commissioner’s appointments or demotions before the decisions are announced publicly. However, he said he never overrules the commissioner’s recommendations.

Unlike with Perkins, however, those demotions were not a surprise: Coleman had faced criticism for a low clearance rate in the Homicide Squad, which he headed. Harrington and Aquino-Gaines were demoted six months after Davis took over and wanted to create his own command staff, rather than work with one he had inherited from the previous commissioner. In May, during his latest command reshuffle, Davis demoted another deputy, Colm Lydon, who officials said asked to be demoted to lieutenant detective.

Demotions from the command staff are not common in the department. Since Davis became commissioner in December 2006, he has demoted three deputies and one superintendent in addition to Perkins. In 2007, he demoted both Daniel Coleman and Gladys Aquino-Gaines to sergeant detective and Superintendent Robert Harrington to lieutenant.

Perkins, who is now assigned to the department’s gang unit, declined a request for an interview because he did not have permission from the department to discuss his demotion. Detective Menino also declined to be interviewed. In demoting Perkins, Davis relied on his unilateral authority as commissioner to decide who serves in his command staff in the role of superintendents and deputy superintendents. Supervisors below them - captains, lieutenants, and sergeants - earn their rank through the civil service process, which requires officers to take a test to show they qualify for the positions.

Boston police officers are barred from speaking with the news media without department approval, but many privately said that, four months later, Davis’s action still evokes confusion and conjecture among members of the commissioner’s command staff. That confusion deepened when Mayor Menino, during a campaign debate in September, praised Boston’s record in guarding against terrorist attacks, noting that the city had been given an award last year from the US Department of Homeland Security. Perkins was the officer picked to go to San Francisco to accept the award on behalf of the Intelligence Center.

The senior Menino, who was briefed by Davis on the changes in the police command staff two days before they were made, said he told Davis, “It’s your decision. I’m not going to get involved in that. If I get involved in that, it’s a political decision, and I have never gotten involved in a political decision on any appointments.’’

Menino blamed campaign politics for the questions being raised now. He pointed out that a key union representing police superior officers endorsed his opponent, Michael F. Flaherty, during the preliminary campaign.

“When the commissioner comes to see me to discuss command staff changes, I always say to him, ‘It’s your command staff; can you live with this? Are these individuals going to be able to carry out your game plan.’ That’s all,’’ Menino said. He added that while he doesn’t like some of Davis’s appointments to his command staff, “I would never say you have to get rid of him. He has to have a team that he has faith in.’’

Menino also acknowledged that he keeps close track of the department’s operations, starting his every workday with a 6:30 a.m. phone call to Davis to check on how the city had fared overnight. Menino has shown a willingness to involve himself in police policies and procedures. Last May he rejected Davis’s plan to arm dozens of Boston police officers with M16 semiautomatic assault rifles.

Perkins, 46, a police officer since 1988, was picked by former commissioner Kathleen O’Toole, to join the Intelligence Center when it was formed in 2005. The center quickly grew from a small unit of eight detectives to a bustling staff of 19 detectives and eight civilian analysts.

Inside the department, Perkins was considered a tough, hard-working leader who delegated authority effectively but could be overly demanding with detectives and sometimes clashed with other supervisors in other units. Outside, he was often the public face of the agency at law enforcement conferences on intelligence gathering and had the respect of police supervisors in the other eight Boston-area communities who are part of Boston’s regional intelligence center, said Paul Upton, deputy superintendent at the Somerville Police Department.

“When you investigate in police work, you develop a list of go to people, they’re the people who you can always rely on that are going to do whatever they can to help you. For me, Earl Perkins was a go-to person,’’ Upton said.

Last year, the US Justice and Homeland Security departments singled out the intelligence center and six other intelligence centers out of 72 nationwide to work on a pilot program designed to improve intelligence sharing without violating citizens’ privacy.

“We would not have made the progress we have with this program without (the Boston center’s) participation,’’ said Thomas J. O’Reilly, a senior policy advisor in the Justice Department, who is overseeing the program and has recommended that some of Boston’s practices be adopted by the other intelligence centers across the country. During the campaign in September, Menino was asked if the city had done enough to keep Boston safe from a terrorist attack.