Does an anticholinergic work on the muscles?

Anticholinergic. You did not specify what anticholinergic you are asking about so I will try to answer specific medication types: a nasal spray does not affect muscles. An inhaled one may produce some bronchodilation by relaxing the smooth muscles in the airways, oral ones usually don't affect skeletal muscles but may affect smooth muscles in the gastrointestinal tract and relax them.