In everyday life, we rarely use both hands to accomplish a motor task. This is one of the reasons why putting with just one hand on the handle can yield positive results.

A drill I give many of my students who are having trouble getting the ball on line is to place a ball at a distance of no more than three to six feet from the hole. Your job is to attempt to make the putt with just your right hand on the putter handle. After attempting five to 10 putts with your right hand, repeat using just your left hand. 

After the left-handed putts, note which hand is more of the control hand. This is the hand you felt more comfortable with or the one that got the ball in the hole the most consistently. 

Often, it’s your dominant hand, which should be no surprise. There are a few golfers who feel the non-dominant hand (the left for right-handers) is better at controlling the ability to get the ball started on line. Whatever is the case, work to get both more capable of controlling the putterhead. If one hand is clearly the winner, it may not be prudent to spend much time on the other hand.