Child Care Protection Act of 2013 - Amends the Child Care and Development Block Grant Act of 1990 to require states that receive funds under such Act to: (1) require and conduct criminal background checks for staff members of child care providers; (2) prohibit the employment of a child care staff member who refuses to consent to a criminal background check, makes a false statement in connection with such background check, is registered as a sex offender, or is a convicted felon involving certain crimes; and (3) provide criminal background checks to child care providers upon request. Imposes a financial penalty on states that fail to comply substantially with the requirements of this Act.