I have no legal education but I would think that if you were an innocent civilian and was attacked by a police dog then you may have a case. If you were being pursued by the police and were resisting or running away, then I think the police would claim that their dog (which is basically considered a member of the Police force) was acting within the law and it would never have happened if you had complied with any request to stop, stop running or stop resisting. Basically it would depend on the circumstances under which you were bitten.