It is a good question. In all problems that you might be facing R C as series components excited by DC source. You know what to do then. Interestingly if they are in parallel ( i am saying just r and c in parallel) it will still be ... well you might have the answer all ready. But what will happen if there is a case where a series RC has a parallel r ..then the idea is to find the equivalent impedance and the time constant will be c*(whatever you get) In this case R+r.
hope it helps