Three top police executives from off-Island are finalists in the search for a new Edgartown police chief.

Robert DeFlaminis Jr., Bruce R. McNamee, and Brian Lauzon will be interviewed Monday by the Edgartown selectmen. The interviews will take place from 1 p.m. to 4 p.m. at the town hall and are open to the public.

Selectmen will meet at 4 p.m. for their weekly meeting, at which they may name the town’s new police chief.

Mr. DeFlaminis is the assistant chief of police for the Massachusetts Port Authority in Boston. Mr. Lauzon is a lieutenant-executive officer at the Natick police department. Mr. McNamee is the captain of the administration division of the Plymouth police department. He was also a finalist in the search for a Chilmark police chief last year.

The three finalists were the top performers in an all-day assessment held Monday on the Island, selectman and board chairman Arthur Smadbeck said.

The candidates will meet Monday morning with members of the police department.

The closely-watched process of choosing a new chief began in early December, when former chief David Rossi filed for medical disability after he had a heart attack. Lieut. Chris Dolby has been serving as acting chief.

Integrity Testing LLC, a consulting company, has assisted with the search along with a community panel including the former fire chief, school principal, council on aging director and human resources director.

The group chose nine semi-finalists from a large field of applicants. Six were selected to take a day-long assessment test on Monday this week. One dropped out shortly before the test, Mr. Smadbeck said.

He said the testing process was grueling. “This was no nonsense,” he said. “I’ve never seen anything like this. This is the way you do it.”

He also said he was impressed by the quality of the applicants. “Really high-powered, highly qualified people,” he said. “I’ve been told that the resumes were just out of the park.”