I would think that the town council would be your best bet, although it depends on how long ago it was. I have 2 mayors in my family, but they were both mayor in my lifetime, so there is no problem in confirming that story.
My great Nans brother was a Town Mayor after 1901. I contacted the local Town Hall to where he lived and they gave me a print out from 1875 until the late 1980's listing each and everyone of them j- at no cost to me.
So try the Town Hall of the town before the actual council.
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