“My aunt passed away and both our names are on a savings account and checking account. I’ve moved the savings account over to the checking account. I am paying her bills using the checking account. Do these monies belong to me now or do they have to go through the courts? Missouri is the state involved”

That will depend on many factors, including how exactly your names are listed on the accounts, and what, if anything, was stated in your aunt’s will. So long as you are using the money (half or more of which may belong to your aunt’s estate) to pay your aunt’s bills, there is probably little issue, but you’ll want to check with a Missouri trusts and estates attorney before using the money for anything else.

Recommended reading (click on the picture for details):
Family Wealth--Keeping It in the Family: How Family Members and Their Advisers Preserve Human, Intellectual, and Financial Assets for Generations