Carrying bat

[blue2u]

I had a situation last night in a men's slow pitch rec. league that I have never seen before.
Batter hits a flyball to center that hits the ground. Runner, seeing that the center fielder isn't rushing to the ball, goes to second still carrying the bat. A sweep tag is attempted and missed, runner continues to third, still carrying the bat. Shortstop throws the ball, hits the runner in the back of the head, ball ends up in left field. Runner finally notices he still has the bat and drops it in foul territory between third a home ( by the way, his head was all right). My question, is there a rule out there saying you cannot carry the bat? and if so, where is it?
The bat was carried in a non threatening manner and did not interfere with the plays in any way.