Terminated for illegal activity

What is the name of your state (only U.S. law)? Michigan
I was recently terminated from my job. I had stolen monies from a client, which was promptly replaced, but nonetheless it was illegal and unethical. Upon termination, I was asked to sign a form which stated I was resigning in lieu of being terminated due to proof that I had stolen monies. I was told if I did not sign the form the company would initiate a formal investigation. Should I have signed this form? I'm unsure what a formal investigation means. I'd like to put this behind me and begin a new. I'm thinking that by signing the form I could do that?

There is no one size fits all right or wrong answer to this question, but it sounds as if you were given a chance to resign in lieu of being fired and probably prosecuted. Which is more than you deserve.