STP in bridged connection
 

I am trying to get a bridged connection to work in centos

here is the network diagram

http://img821.imageshack.us/img821/8598/98687182.png


there are two interfaces in linux system , they are bridged and connected to the windows system
I am not sure if I need to enable STP in the bridge or not?

well you'd only enable STP if there is a risk of creating a bridge loop, and it would suggest from your funky diagram that that's not possible. Having said that, if there is no spanning tree domain already running on those network segments, it'll be totally benign if it is running.