May not be a Federal law, but this is the info for Maine:

PART 3. ELEMENTARY AND SECONDARY EDUCATION
CHAPTER 223. HEALTH, NUTRITION AND SAFETY
SUBCHAPTER II. IMMUNIZATION

20-A M.R.S. § 6354 (2003)

§ 6354. Immunization
1. IMMUNIZATION REQUIRED. Except as otherwise provided under this subchapter, every parent shall cause to be administered to his child an adequate dosage of an immunizing agent against each disease.

2. IMMUNIZING AGENT TO MEET STANDARDS. Any such immunizing agent shall meet standards for such biological products, approved by the United States Public Health Service and the dosage requirement specified by the Department of Human Services.

20-A M.R.S. § 6355 (2001)

§ 6355. Enrollment in school
A superintendent may not permit any child to be enrolled in or to attend school without a certificate of immunization for each disease or other acceptable evidence of required immunization or immunity against the disease, except as follows.

1. WRITTEN ASSURANCE. The parent provides a written assurance the child will be immunized within 90 days by private effort or provides, where applicable, a written consent to the child's immunization by a health officer, physician, nurse or other authorized person in public or private employ.