Anthony DeJuan Boatwright Act - Amends the Child Care and Development Block Grant Act of 1990 to require a state to include as part of its regulatory process for issuance and renewal of licenses to providers of child care services, a recommendation to each provider that it carry current liability insurance. Requires state plans for the use of child care and development block grant funds to certify that there are in effect state or local health and safety requirements that each child care provider: (1) post publicly and conspicuously in the service area of its premises a notice specifying whether it carries current liability insurance; and (2) give written notice to parents about whether it carries such insurance, obtain the signature of at least one parent per child acknowledging receipt of such notice, and maintain records of such signed notice while a child receives services and for one year thereafter.