Vernon residents narrowly voted on Town Meeting Day to dissolve their police department, and were given $40,000 to find police coverage elsewhere as of July 1.
Vermont State Police say that would get the town 12 hours of coverage a week.
But now, some residents say the plan won't work. They are circulating a petition that calls for a special meeting to reconsider the town budget and police spending.
Select board members say they were forced to slash the town's budget in anticipation of Vermont Yankee's closure.