Birmingham police began making plans last year for the devices to be carried by school resource officers, but none has been deployed so far.
Kincaid said recent reports of health dangers from the shock delivered by the guns have made him question whether it's wise to put them in schools.
A teenager in Florida died in late December after he was zapped with a Taser, the third person to die there in a month after being shocked.
"We've had incidents of people being killed," Kincaid said in an interview after Tuesday's City Council meeting. "I would think the children would be more vulnerable. If you tazed in a hostage situation and a person dies you can almost be forgiven, but if you tazed in the school situation, notwithstanding what the facts are, I just don't think you'll be able to be forgiven for that."