Any child care center or group child care home that is licensed with a preschool endorsement, in accordance with regulations adopted pursuant to § 19a-79, may deem a child who is thirty-two to thirty-six months of age, inclusive, to be three years of age for purposes of enrolling such child in a preschool program provided by such center or home, provided such center or home receives written authorization from such child’s parent or guardian and the program director to so enroll such child in the preschool program.