Six years after Muttontown pulled out of a multivillage North Shore police department, Upper Brookville is questioning whether it and four other villages in the consortium pay too much for police protection and the sixth remaining village pays too little.

Upper Brookville’s board of trustees on Jan. 26 called for an independent study into how funding for the Old Brookville Police Department is allocated. The current formula is based upon each village’s assessed property valuations.

In a Jan. 20 letter to Upper Brookville residents, village officials say the formula, which has been used since the department’s formation in 1949, “no longer is a good predictor of the demand for police protection.”

A formula that includes factors more closely tied to demand for services — such as population, miles of roads and number of police calls — would increase costs for the largest village in the consortium, Brookville, and decrease expenses for Upper Brookville, Cove Neck, Matinecock, Mill Neck and Old Brookville, according to calculations by Upper Brookville Mayor Elliot Conway.

Conway said the alternative formula is not a formal proposal. An independent study conducted by experts that includes an examination of other intermunicipal agreements would provide a neutral analysis, he said.

Muttontown left the Old Brookville department in 2011 after village officials complained it was contributing the most money to the police budget, but had no greater voice in operational decisions.

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Some Upper Brookville officials then proposed looking into leaving the department because of concerns about added costs from Muttontown’s departure and rising police benefit costs, but the village opted to remain.

Conway praised the professionalism and service of Old Brookville police. He said he’d prefer the village remain in the consortium. But, he said, if an independent study finds the village is paying too much, “there’s a possibility there’d be a groundswell of support from [Upper Brookville] residents . . . that might include looking at other local options for police protection.”

Upper Brookville and the other five villages have in the past several weeks approved a five-year renewal of their joint protection agreement for Old Brookville police, Conway said. The agreement includes a clause that villages consider a study on allocations, he said. Any potential changes in allocations would not take effect until 2022, when the next agreement is signed, he said.

Mill Neck Mayor Peter Quick said he doesn’t view the current allocations as unfair. A system based upon the value of property is a common way to determine expenses for shared services, he said.

Nassau County police use assessed valuation to allocate taxes, said police spokesman Det. Lt. Richard LeBrun.

Even so, Quick said, “I’d certainly be open to looking into other methods of allocation. . . . I don’t think there’s ever any harm in looking at different ways of doing things.”