As much I know there is no place in CRM where you can find the class associated with the Object.
I use the following procedure to find the class.
In SE24 TC I typed cl_crm*compl*run_btil and press f4 this gives me the class name and then I put a break-point in this class and check whether its being called or not from UI. If its called then its the correct class.
Thanks
Kumar.