Book Stamp Act

Book Stamp Act - Directs the Secretary of Health and Human Services (HHS) to establish a grant program (based on certain State allocations under the Child Care and Development Block Grant Act of 1990) to promote child literacy and improve children's access to books at home and in early learning and other child care programs, by making books available through such programs.

Requires State agencies to use such grants to enter into contracts with local child care resource and referral agencies to: (1) provide payments for eligible early learning program and other child care providers, on the basis of local needs, to make books available; and (2) promote child literacy and improve children's access to books at home and in early learning and other child care programs. Allows State agencies to reserve a portion of grant funds to support a public awareness campaign relating to program activities.

Amends Federal law relating to the U.S. Postal Service (USPS) to require USPS to establish special postage stamps for child literacy, at the regular first-class rate plus a differential amount, for voluntary use by patrons. Requires USPS to pay certain amounts raised by stamp sales to HHS for child literacy promotion activities.