The child, Olivia Raspanti, died March 17 at the Carousel Day School in Hicksville.
State officials shut down the center the next day, saying there were no records of the facility being issued a license to operate a day care center.
Formica said the school was in compliance with all state day care regulations but never applied for a license.
Attorneys for Formica and Cordaro did not immediately return calls for comment.
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