Dropped bat interferes with play at the plate

[Guest Larry Bond]

In an MLB game, the bat was dropped so that it landed partially across home plate. Immediately afterward, a runner tried to score from 3rd base while the bat was interfering with the catcher’s tag. 
Since the play developed so quickly, there was hardly time for either the catcher or the umpire to have moved the bat out of the way. 
In this case, the catcher was able to make the play anyway. However, what if this hadn’t been the case? Who is responsible? Would the batter have been called out for interference, or would the run not have counted due to interference? 
I’m looking for an official rule applying to this situation.

Thanks!

Larry Bond

[Replacematt]

41 minutes ago, Guest Larry Bond said:

In an MLB game, the bat was dropped so that it landed partially across home plate. Immediately afterward, a runner tried to score from 3rd base while the bat was interfering with the catcher’s tag. 
Since the play developed so quickly, there was hardly time for either the catcher or the umpire to have moved the bat out of the way. 
In this case, the catcher was able to make the play anyway. However, what if this hadn’t been the case? Who is responsible? Would the batter have been called out for interference, or would the run not have counted due to interference? 
I’m looking for an official rule applying to this situation.

Thanks!

Larry Bond

There isn't one. The bat exists, and it's the responsibility of players to play it.

There are provisions for a bat thrown into the playing area or a bat that hits the ball a second time, but those doesn't apply here.