There's no call to be made for the puck hitting the goalie on the attacking side of the center red line. A minor penalty is to be called for deliberately handling the puck on the attacking side of center ice.
Not Mike C
Not Mike C is correct. Rule 407 (e) states:
"If a goalkeeper deliberately participates in the play in any manner when he is beyond the center red line, a minor penalty shall be imposed upon him."
If the goalie would have continued to his bench, after the puck hit him unintentionally, without shooting the puck back down the ice, he would not have received a penalty.
Staff
A goaltender is heading to his team bench in the dying seconds of the game to add the extra attacker in an attempt to tie up the game. His bench is located furthest from his net, so he has to skate through the neutral zone to get there. As he is passing the center red line, the opposing team fires a shot at the open net and it hits the goalie. The goalie then shoots the puck back down the ice. What call, if any, should be made?