Karen Taylor, whose adult son was attacked in a downtown parking garage, started the petition to submit the ordinance.
"You know that the community at large supports this issue, and even one violent crime like what happened to my son is too much," she said at the council meeting on Monday.
The ballot initiative wouldn't fund cameras on streets downtown, but rather would allow for their placement if money becomes available.
Cameras are already allowed in downtown parking garages.
Opponents of the measure, including members of City Council, said general downtown cameras would be ineffective and brought up the possibility of a "Big Brother" mentality.
Will you vote for or against having surveillance cameras in downtown Columbia?