If you want to say that "he put one of his hands on one of her shoulders", Then you can say, "He put his arm on/over her shoulder" if it looks like this : http://www.flickr.com/photos/steffe/7862869732/ But you will say "He put his hand on her shoulder" if it looks like this : http://www.liesyoungwomenbelieve.com/assets/images/hand%20on%20shoulder.jpg so there is a slight difference between the two and you need to chose accordingly.

It depends on the situation and where he and she are. If he is standing beside her (to her left, say), facing the same direction and puts his right hand on her left shoulder, then "He put his hand on her shoulder." If he is facing her directly and puts both his hands on both her shoulders, then "He put his hands on her shoulder." Of course, putting his (one) hand on her shoulders is physically impossible.

He put his hand on her shoulder. Also possible: He put his arm over her shoulder

He put his hand on her shoulder.

Thank you. It seemed logical to me , too.