The New York Archdiocese is investigating the FDNY commissioner’s Catholic-school-teacher daughter and her principal boss because of their Twitter conversation with her disgraced EMT brother, who was posting racist messages.

A spokeswoman said the archdiocese’s superintendent of schools is probing the Twitter exchange among Theresa Cassano-Pitre, Joe Bollini and her brother, Joseph Cassano, who wrote to his sister, “Good luck today with all the little shwoogs,” invoking a racist slur. Both Cassano-Pitre and Bollini responded. Neither could be reached for comment.