The Wiki page suggests that the only operational Tiger P was assigned to the 653rd Heavy Pzjgr battalion as a command tank. The battalion was pretty bloodied during Kursk and the following retreat, Im not sure if the Tiger P survived, but the unit was redesignated afterwards.

During its lifetime, it was attached to the 41st Pz Corps. In what manner it was attached, I dont know. Id doubt that it was attached to a division or brigade, rather the unit was probably a seperate AT battalion which would be temporarily attached to field units depending on the given situation.

Id look at David Glantz's Kursk book, or its appendices, to see if the unit shows up in his OOBs.