Does the 13inch macbook pro Mid 2010 run windows 64 bit or 32 bit?

I would say that your hardware should support either 32 bit or 64 bit, but it would reallly depend upon your processor. If you have a Core 2 Duo, or Core i3, Core i5 or Core i7 processor in your MBP, then the processor is 64 bit, and your machine should support a 64 bit OS...

64 bit. There is no reason to run 32 bit Windows.

Your computer is 64 bit

1. New applications/programs are 64 bit

2. 64 bit Windows runs 32 bit applications/programs

3. 32 bit Windows can only use between 3 and 4 GB of RAM. If you have or plan to have more than 3 GB RAM then you must use 64 bit Windows in order to use all your RAM