Almost all adoptions are "closed" adoptions. Do you mean "private" adoption? This sounds more like a private adoption. Call the county where the adoption took place. Sometimes it is different than where the person was born. Ask, if in fact, they have record of the adoption.
Your father is going to have to do this. You, as his child doesn't have the legal right. It would be different if he were deceased.
Search the web for "adoption laws by state" and find out the laws of Montana. Usually they have a registry and also offer the CI (contact intermediatery) program, in which, the CI has the adoption file, or records, therefore has all the names, dates, address, etc and can contact the birth mother, father, family, etc. They can also tell you if the person is deceased, etc. This usually costs about $250.00 but all states are different. This is the easiest way to go and believe me is way cheaper than an attorney.
It would also help if you would post your fathers date of birth, the cities and counties involved and his full adopted name. For anyone to help you search, they will need this info.
I spent 29 years searching for my brother before I found him so I know how frustrating it can be.
Chances are your father has half siblings and it is very possible they are looking for him. Maybe even his birth parents? They could have been searching for years.
Jennifer