Count the Vote Act This bill authorizes an individual to file a complaint with the Department of Justice (DOJ) for certain violations made by a state with respect to federal elections, such as for violations of required voting system standards or failure to provide provisional ballots. Currently, individuals may file such a complaint through a state-based administrative procedure. Further, DOJ must immediately provide (1) a copy of the complaint to the entity responsible for administering the state-based administrative complaint procedure for the state involved in such complaint, and (2) a copy of the response to such entity. The bill also permits such an individual, including an individual who seeks to enforce their right to a voter-verified ballot, to file a civil action for deprivation of rights.