If you are a Public Official you can not block peoples comments. Colorado Senate President Leroy Garcia blocked a commenter on Facebook and was fined. Who paid for it? We did the taxpayers money. According to the Colorado Sun Leroy Garcia, as part of the agreement agreed not to block or delete facebook users from his public account.

This all came about when Alexander Armijo made comments on his page and then was blocked. Alexander Amijo sued and said his First Amendment rights had been violated. According to Garcia's Attorney all comments, offensive or vile, are required to be published on an elected official’s page.”

If someone makes a comment on his personal page he can delete what they said however since it was not his personal account and his official Facebook page he cannot delete someone or their comments.