Military Ballot Integrity Act of 2012 - Amends the Uniformed and Overseas Citizens Absentee Voting Act to require states which do not transmit to an absent uniformed services voter a validly requested absentee ballot for a federal election by the deadline required to delay the certification of the election results by the number of days by which the state missed such deadline with respect to the voter, except in elections subject to a state undue hardship waiver.
Allows any person aggrieved by a violation of the Act to bring a civil action in an appropriate district court for necessary declaratory or injunctive relief. (Under current law, only the Attorney General may bring such an action.) Allows for the award of reasonable attorney's fees for the prevailing party.
Requires a report from the Attorney General in each year in which a general election for federal office is scheduled on the number of attorneys and other staff within the Department of Justice (DOJ) assigned to enforce the Act, as well as a plan to detect noncompliance by state and local election officials with requirements of the Act.
Requires the presidential designee responsible for federal functions under the Act to establish and operate a centralized mail forwarding database through which balloting materials for a member of a reserve component called or ordered to active duty are forwarded to the member's correct mailing address after the member is released from active duty.