I don't know of any hospital that has ever checked my credit before hiring me. If you read the fine print on the application before signing it, it will say if you are giving them permission to obtain credit history.
The only employer that I know ran a credit report was back in my banking days.
However, the Board of Nursing for your state will check your criminal history before issuing your license. If you have any felony convictions, that may prevent you from obtaining licensure. In most cases, they will ask for the circumstances around the conviction, and make a decison based on this. Whatever you do, don't lie about it. They will check into it. If you are worried about it, you may contact the board before investing your time and money in nursing school
I hope this helped. Good Luck.