It's been a while since you posted this so perhaps you have already gotten an answer and found your ancestors records. As a retired police officer I can give you a little insight on your search. Realize first that every jurisdiction may present different challenges but here are some general thoughts. He might have been arrested by any of several law enforcement agencies....perhaps a city police department, or the county Sheriff, State Police or perhaps even a federal agency (if he were in violation of federal liquor tax laws for example) If he were arrested by State, County, or local police then you should be able to find a record in one of the local courts. Many places have more than one court and you will need to check with the County Clerk to determine the number of courts and which one would most likely have been the presiding court for that sort of arrest.
Had someone come to our police department seeking information on an arrest that happened 40 or 50 or more years ago we would have had a very difficult time producing information since those records have been moved into storage and none of those old arrests were ever digitized. It would involve sorting through a lot of paperwork, If you were lucky we would have been able to find an "arrest card" in an alphabetized file. As I recall we used to purge those cards from the file if we knew the person was deceased. Saves space, but doesn't help future researchers much. Different states have different public records retention laws affecting police departments so your luck in locating information will vary from place to place.
Looking for the court records would also be a challenge for the same reasons, not knowing a year would make it especially difficult to find as you would need to search docket book indexes one year at a time and each court would have their own set of docket books. Knowing at least the year of arrest(s) would help a great deal. If he had served time in a state prison your search would be a lot easier, many states have digitized their old records and can do a search on a name pretty easily. I found a distant cousin who served time in the Nebraska state Prison in 1909 without much difficulty. I initially discovered that incident from a newspaper article I accidentally discovered. Local newspapers often record crime stories and arrests....but again you will need to have a date or at least something close in order to search through the old papers.