Child Safety Act - Authorizes the Secretary of Health and Human Services to award grants to and enter into cooperative agreements with public or private entities for the establishment and operation of supervised parent and child visitation centers. Sets forth provisions regarding: (1) the use of funds; (2) application approval requirements; and (3) project evaluation. Authorizes the Secretary to award grants to study supervised visitation with regard to sexually abused or severely physically abused children. Authorizes appropriations.