I came across a GA gubernatorial campaign sign on the government property (public library). Is this legal? This place is funded by the taxpayers and they are very split on the election candidates.
Under OCGA 16-7-58, it is unlawful to put signs
On any public property or building, unless the owner thereof or the occupier as authorized by such owner has given permission to place such posters, signs, or advertisements on such property; provided, however, that signs within the rights of way of public roads shall be governed by Code Section 32-6-51
If permission was not granted, it is illegal.
Permission could be granted, insofar as there is no basic constitutional provision prohibiting dissemination of political ideas on public property (quite the opposite, in fact). A problem would arise if the government (via an official) allowed only candidate X to put up signs. Allowing political speech is not a problem, forbidding it is a problem (w.r.t. the First Amendment).