If it is an account on your credit report I am going to assume that means you could access the credit there and so it is also your account (albeit joint) as far as credit reports go. (In contrast my wife is authorized to use her company's card but it does not show up on our credit reports.)
If the account is in good standing then closing it may well lower your credit score, but that is not guaranteed. It will reduce the average age of your accounts, which will hurt your score. However, it will also reduce your total credit available, and if you have too much credit available at the moment that could be a plus for you.
The second effect might be counter-intuitive, so as an extreme case imagine your father has a $100,000 credit limit and you are approaching a credit union for a $10,000 car loan that would personally be a stretch for you as a new college graduate. The CU might be comfortable giving you the money for the car if the $300 you owed them each month was your only debt payment. But the fact that on paper it looks like you could go rack up $100,000 worth of credit card debt on the way home with a $2000 monthly minimum payment would worry them.
If you are really interested there are some credit monitoring sites that you can go to and play "what if" with that can give you a reasonable guess of the effect. The actual formula used by the credit scoring agencies is proprietary and not shared so remember that in the end whatever they tell you is just a good guess.