Terminated without cause?

What is the name of your state?Ohio
I was terminated approx. 1 month ago without notice (company has at-will policy). My termination letter stated that I did not meet my job responsibilities. This letter was not signed by anyone. When I asked managment to explain what job responsibility that I did not meet or surpass, they refused to answer and asked me just to sign and date the form. I refused to do so because I did not agree with them. Since my termination, present employees have been asked not to talk to me and have been asked to the office a few times since and questioned if they have. The gossip that has been told recently to several employees, is that I did something really bad to get fired. Last week when submitting for unemployement, the agency stated that my employer claims that I got in a fight/argument with them, which is untrue. I have also been told by 2 present employees that they heard something had been put in my file since my termination.
Do I have any rights at this point to see my personal file?
Do I have any rights to accuse them of slander?

Do I have any rights at this point to see my personal file? No. Ohio reg's only require that you be given access to any medical records the employer has on you, such as the results of a physical exam.

Do I have any rights to accuse them of slander? You can accuse anybody of anything. If you're asking if you have the basis of a claim for slander, the answer is no. (a) You have no facts to base a claim on; all you have is gossip and third hand information. You have no idea what, if anything, the employer has actually said about you. (b) You have not experienced any damages.

You can't base a suit for slander on something the employer told the UC Division.