Conversations in the workplace aren't always business-related, nor are they always productive. Such is the case when one of your co-workers reports that she overheard another co-worker expressing racist comments about you. The question is whether you believe what your co-worker is telling you or if she misinterpreted something she overheard. The quandary you're in could make things far more complicated, unnecessarily so. Out of all the ways to handle this, avoid jumping to conclusions and keep calm, even if you know you would be terribly hurt if you heard the comments yourself.
The co-worker who reported what she overheard may have been telling you to get a reaction or to encourage you to take action. Even if you didn't hear the comments yourself, it's natural to experience a range of emotions. You could be in disbelief, first of all, because you didn't hear the comments yourself, and you aren't sure whether your co-worker actually overheard a racist comment. Or, you might be angry at the co-worker who thought it was necessary to share this information with you. Confusion and sadness also are emotions you might feel, depending on the kind of friendship you have with the co-worker who claims to have overheard the comments.
There's no telling why your co-worker felt it was necessary to share this information with you, but if she intended for you to respond or take action, the onus is on her to step up and attest to what she overheard. If she decides to disclose exactly what she heard, she faces possibly being alienated by other employees in the company. Regardless of age, tattlers usually aren't highly regarded or respected, and they're often described as troublemakers. If you ask your co-worker to provide the information to your human resources department, don't be surprised if she recoils from her original remarks.
Suppose your co-worker isn't willing to speak to HR on your behalf to report what she heard. Ask if she's willing to tell you what she overheard and who she believes made the comments. Still, she might be reluctant if she suspects that you'll confront the person. It's up to you whether you will confront the person, but simply knowing who might have made offensive remarks might actually give you some insight. She might disclose the name of someone with whom you don't have the best working relationship or someone you've suspected is biased.
The point you should resolve isn't with the person your co-worker claims made a racist comment. You must have a talk with the co-worker who came to you with the news instead of reporting what she overheard to the HR department. Remind her that even someone who isn't the target of racist remarks can report such comments to the HR department. If you have what you thought was a friendship with her, ask why she felt obligated to tell you if she wasn't going to stand up for you or honor your friendship. The chance you take is that she'll no longer confide in you, but if all she's confiding are hurtful -- or, maybe untruthful -- remarks, then severing the collegial relationship could be best.