Parents have this authority via RSA 197:2 (in single town school districts), and RSA 195:13 (in cooperative school districts), to call for a special meeting (i.e. special election) so voters can vote to override the school board.
https://www.tmbfiles.com/parents-have-this-authority-via-rsa-1972-in-single-town-school-districts-and/
https://www.thegatewaypundit.com/2021/09/hidden-laws-enable-parents-control-school-boards/