Possibly, but it is expensive to do so and takes time. The most efficient way to handle this is to have the problem taken care of and present the bill to landlord. If they refuse to pay, then sue them in small claims court for damages. Be sure you keep all evidence of your problem and have some witnesses, if possible.
If the feces/urine in the attic is bad enough to affect your health, you may have grounds to breach your lease on the grounds that the home is uninhabitable. Before you go this direction, consult with a local attorney about the specifics of your case and the extent of the problem. Even if the infestation is not active, the residue from the infestation may affect your health.
I am not your attorney and the advice given may be dependent on facts and circumstances that are unique to your situation. I am providing this free advice as a public service, and not specifically to be acted upon. If you would like advice specific to your case, please contact me.