You can research your state's fence laws, either online or in your local public law library. A good place to start is the Legal Research area on Nolo's website. You may also want to check your city or town's laws. For tips on how to do this, see Nolo's information on How to Find Local Ordinances and State Laws
For a comprehensive guide that contains more specific information on landowners' rights and responsibilities with regard to fences, see Neighbor Law: Fences, Trees, Boundaries & Noise, by Cora Jordan and Emily Doskow (Nolo).