MADISON — Town officials are in discussions with the Somerset County Sheriff’s Office on possible changes to how the office provides law enforcement coverage in Madison.

The discussions center on the ongoing struggle law enforcement agencies in Maine are having with hiring and retaining qualified officers.

For at least a year, two deputy positions have been open at the Madison Division of the Sheriff’s Office. Officials said hiring for the Madison Division has been difficult because jobs elsewhere are considered more attractive.

Somerset County Sheriff Dale Lancaster met last month with the Madison Select Board to review options for ensuring the town receives proper coverage.

Lancaster proposed an expanded budget of $613,000 for the Madison Division that would include three patrol deputies, a school resource officer and an administrative position working 32 hours a week. But rather than permanently assigning deputies to the division, they would be assigned in shifts that rotated every two weeks.

“I think this change of model would give us better coverage, and we wouldn’t always be looking for that coverage,” Lancaster told the board in November.

The $613,000 budget proposal would represent an additional $83,000 for Madison taxpayers, although Town Manager Tim Curtis said he hoped to bring that amount down.

Voters in Madison approved a $3.45 million municipal budget in June, with a policing budget of $440,000.

“We have some streams of revenue to make up the difference (to taxpayers),” Curtis said.

The Madison Police Department was disbanded in 2015 and the Madison Division of the Sheriff’s Office was formed to cover the town’s law enforcement needs. The town pays the county for operations and oversight as part of the agreement.

The decision was a cost-saving measure approved by voters and initially called for five full-time deputies and one assistant executive secretary. The town at the time was facing several issues, including concerns about Madison Paper Co., which closed the following year, resulting in a property tax increase.

Curtis said he has prepared an estimated budget for what it would cost to bring back the Madison Police Department. He said hiring a full-time police chief, four officers and an administrative position would cost about $700,000.

“The current shortage of law enforcement candidates at every level would make it very challenging to start from scratch and hire new,” Curtis told the Select Board.

Selectmen postponed a decision on altering the agreement with the Sheriff’s Office, saying they did not want to make a significant financial decision in the middle of the fiscal year.

At least two police departments in Kennebec County are offering incentives to lure experienced officers.

Gardiner is offering $15,000 signing bonuses to fill vacancies, citing the struggle to fill positions from a pool of applicants that is not expected to grow.

And in Waterville, the City Council voted in October to ratify a collective bargaining agreement with the Maine State Fraternal Order of Police that increases patrol officers’ wages and gives them a retirement plan that includes a cost-of-living increase.