It is the law to carry your passport with you at all times when a visitor to Turkey.
There are permanent Jandarma check points in the area, notably one at the top of the hill as you come into Ovacik.
I live in Ovacik and pass this point twice a day just about every day of the week. It is rare to see it empty of stopped vehicles and of course I am stopped frequently.
I have seen many tourists being taken into the station house there, one can only presume because they do not meet criteria in some way.
Polis also have frequent road checks of ALL vehicles and would want to see your passport too.
I've lived here over 5 years, carry mine and my husband's passports and ikamets (residency cards) with me EVERYWHERE. Sometimes the Jandarma/Polis want to see our ikamets, sometimes our passports. If we didn't have ikamets, it is certain that they would insist on seeing our passports.