There are hundreds or thousands of municipalities of various kinds and sizes in any given state: it's imposible to say that there are none which would require this. As a general matter, though, I am not aware of any which do--it's left to the business's discretion. Obviously, it is a good idea for a business to do so--a business wants customers to know when it is open. To check the rules for a given municipality, try calling the town or city clerk's office.