Alabama’s Fair Campaign Practices Act includes provisions requiring disclaimers.   The Secretary of State’s website describes these requirements and asks:

Does the U.S. Supreme Court ruling in McIntrye v. Ohio Elections Commission affect FCPA disclaimer requirements?
That case, which involved an individual who distributed anonymous leaflets opposing a proposed school tax levy, has very limited impact. Alabama’s attorney general has written in AG’s Opinion 95-218 that the ruling is limited to individuals who distribute anonymous written material (particularly leaflets) in a non-candidate election. In all other circumstances, the advertising must carry identification.

The Attorney General’s 1995 opinion is available online.