No. The library may have purchased public performance rights with a video. Nevertheless, the Copyright Act allows you to play a video in a classroom "for educational or training purposes" (sec. 29.5).
"It is not an infringement of copyright for an educational institution or a person acting under its authority to do the following acts if they are done on the premises of an educational institution for educational or training purposes and not for profit, before an audience consisting primarily of students of the educational institution, instructors acting under the authority of the educational institution or any person who is directly responsible for setting a curriculum for the educational institution:
(d) the performance in public of a cinematographic work, as long as the work is not an infringing copy or the person responsible for the performance has no reasonable grounds to believe that it is an infringing copy" (sec. 29.5).
Copyright Act (R.S.C., 1985, c. C-42)