My grandmother had Hashis and my mother is HypoT and she has had RA for 5 years - really bad RA combined with OA. She might very well have Hashi's too, but the doctor never tested more than her TSH and put her on eltroxin.
There are a number of blood tests that can be done to help determine if you have RA. The main one is RA factor, but not everyone with RA will test positive for this. There is a new test however, called anti-CCP antibodies. These antibodies are present in many people with RA before they even begin to show symptoms.
Seeing as they are both autoimmune diseases and these tend to travel in families I wouldn't be suprized to hear that there are people who have a history of both.