Cyclopentolate can affect how some other medicines work when they are taken at the same time, and propranolol is one of them. The leaflet lists several others as well, including antihistamines, isoniazid, MAO inhibitors, phenothiazines, procainamide, disopyramide, quinidine and tricyclic antidepressants.
These medicines are often taken together with some care. Your doctor may change a dose, space them apart or check on you more often. Make sure your doctor and pharmacist know you take both.