Thank you for your question.
When someone is saying false things about you that damage your reputation, you have a claim agianst the person making the statements for defamation
of character. I assume from your question that fraternization with other company employees is prohibited by the company. If this is true, then given your position in HR, this is definitely defamatory.
If you are aware of who is making the statement, you may sue them directly or simply send a CEASE and DESIST
letter to them warning them that if they continue making false allegations against you that you will sue them.
Also, being falsely accused of a sexual relationship with a co-worker could be seen as a form of sexual harassment
. You should notify your supervisor of this fact as well and ask that your supervisor take action to stop such rumors as it is creating a hostile work environment in violation of your rights under federal law.
Please let me know if you have further questions regarding this issue. Please also remember to rate my answer positively so that I might be compensated for my work on this question.