Fences do not require a building permit. They are, however, subject to Unified Development Ordinance height regulations in Article 9.9: http://www.codepublishing.com/NC/Durham/#!/9.9.html#9.9 There may be additional restrictions on the placement of fences and walls due to easements, stream buffers, and sight lines. It is also important to check with your homeowner's association, if you have one, as they may also have an approval process.