You can potentially sue your co-worker for slander, but it is strongly recommended that you first speak with an attorney who has experience handling defamation of character cases. There are a number of questions that are critical that an attorney would ask you before he or she would be able to recommend filing a complaint. First, does the co-employee allege that others witnessed this alleged racial comment? Second, did anyone believe the defamatory statement made against you? Third, were you damaged in any way due to the defamatory statement (e.g. lose your job or suspended)? Fourth, do you have any witnesses who were present during the conversation where you allegedly made the racial comment? Fifth, do/did you work for a public entity (e.g. town, county state job)? An attorney's advice as to whether or not you have a case depends on how you answer the above (and additional) questions.
Finally, here's a link to the NJ Civil Jury Charge for private defamation of character so that you can obtain an understanding of what you need to prove for such a claim: http://www.judiciary.state.nj.us/civil/charges/3.11B.pdf
I think I addressed a version of this question in a previous post but you recieved great advice in this post as far as questions to ask yourself when considering suing for defamation/slander.
A consultation with an employment or civil tiral attorney would be of great benefit in determining whether you have a case and if so, what recovery you would be entitled to recieve.
As I stated before, be sure to have all of your proofs/evidence in order and give a timeline of what happened so the attorney you speak with can assess the value and merits of your case. Have your tax return, employee manual, and any correspondence you received from your former place of employment ready to go at the consult, should you choose to schedule one.
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