The boards of trustees of the Gilbert School, Norwich Free Academy and Woodstock Academy shall provide for their students special education programs required to be provided by local and regional school districts in accordance with sections 10-76d to 10-76k, inclusive, and may charge any sending town for the costs of any such special education provided to a student for whose education such sending town is responsible and the sending town shall be eligible to apply for state payment for such costs under section 10-76g.