Well, guess, what? In my research, I stumbled across a little article in that area newspaper, the Benzie Banner. Back in June of 1932, they DID have their own police force. Sort of...
New Village Marshal on Duty in Beulah
Those who have a tendency to be naughty are warned to watch their step hereafter while within the confines of Beulah. The newly appointed and commissioned village marshal, Ed Reddick, began his duties yesterday, June 15, and will continue actively thereat for the next three months. That should be sufficient notice to any and all who have been getting a bit careless with local ordinances lately.
A committee is being organized to locate a liberal quantity rustproof and highly resplendent metal from which to manufacture a suitable badge for the new official, and another carefully selected group of citizens has agreed to scour the woods for a husky white ash or ironwood log from which to fashion an adequate club. Prices are also being sought on a conventional streamlined derby and a choice assortment of brass buttons. Meanwhile, the police force began his new duties by painting the park benches a handsome Irish green.
You'll notice that local papers in those days could be very tongue-in-cheek. Although there was almost never a byline, every story had a clear "voice" and very often different voices for different beats. Even the hard news stories often felt a little gossipy, as though hearing the news from your neighbor over the back fence.
As for Marshal Reddick, his three month term implies to me that he's there to help deal with the summer people. While some aspect of the resort business had been important to that part of Michigan for some time, it was around the 1920s that it seemed to pick up for Beulah.
I was curious to see if Ed Reddick was hired from in the community or outside it, so I looked him up in the 1930 census. Beulah, at that time, was too small to have it's own designation in the census, so those residents were listed in the larger township, Benzonia.
And yes, Ed Reddick did appear, two years before his appointment to the job, along with his wife Rose and son, Ed jr. However, they were crossed out. I suspect this was because they themselves were summer residents. The census taker started to take their information, and then found out that they didn't actually live there. (There were other Reddicks in the area, perhaps relatives to visit.)
This, of course, would be another fun detail to use in a cozy mystery: the town marshal being a tourist hired to deal with the other tourists, and expected to leave the townfolk alone.
Well, back to my research... see you in the funny papers!