No arrests have been made. Police and school officials declined further comment on the matter involving Julie Bartolomeo, 45, a Board of Education member since July 1, 2011, who resigned Wednesday.
Bartolomeo could not immediately be reached for comment.
The school posted a notice on its website saying: "The Board of Education has been made aware of information and allegations regarding Mrs. Bartolomeo in recent days.
"The Board was then obligated to share this information with Suffolk County Police. Therefore, the district cannot comment further as this matter is now being investigated by the police. All other questions should be referred to the authorities."
The district said on its website that Bartolomeo's letter of resignation did not specify a reason.
In a May interview when she was running for the board, Bartolomeo said she was a special-education aide in the school district at Bower Elementary school, which has been closed by the district.
She said she was active with the Lindenhurst Soccer League and the PTA at several schools. She and her husband, James, have two children in district schools.
School officials said the vacancy that now exists on the nine-member Board of Education will be discussed at an upcoming board meeting. A board typically has three options in addressing a mid-school-year vacancy: making an appointment, holding a special election or leaving the seat unfilled until the next election.
More information will be provided on this matter in the coming days, school officials said.