Depending on what state the deceased person lived in--or owned property in--you may need to file an estate tax return with the state. You're more likely to have to file a state return than a federal one, because the threshold for owing federal estate tax is so high. (Currently, only estates worth more than $5 million may be subject to federal estate tax, and many of those large estates don't owe tax because of various deductions.)
Most of the states that impose their own estate tax set the threshold at $1 million, though in some states smaller estates are taxed and in others, only very large estates feel the tax bite. State tax rates are much lower, too. In most states, they top out at 12 to 16%, compared to the top federal rate of 45%.
If the estate you're wrapping up must file a state estate tax return, it's time to call in the experts--find someone who has extensive and recent experience with your state's tax code. This isn't a job to entrust to your usual income tax preparer unless that person has unusually impressive credentials.