The penalty would be a $100 fine.
If it passes, New York would become the second state to ban texting and driving. So far, Washington is the only state to outlaw texting. That ban takes effect in July.
People in New York state are already banned from talking on their hand-held cell phones while driving.
State Senator Carl Marcellino, of Long Island, was a leading supporter of the measure.
Those in support of the bill say texting while driving forces drivers to take their eyes off the road, leading to accidents.
