Most cities have rules and laws governing what kind of businesses can be operated in a residential area. The idea behind zoning regulations is to maintain property values by keeping out the noise, pollution, extra traffic, or any other possible nuisances a business might generate.
Zoning regulations are established locally, and tend to differ from town to town.
To find out about zoning laws in your area, you can look in the local phone book, in the government section under "zoning" or "planning". You can also call the central administration number for your town or your county or city clerk to find out who to talk to.
You can also request a copy of the zoning law governing your area from the city clerk's office. There may be a copy of this in the local library as well.