False allegation against me?

recently, there i had a customer come forward with a falso allegation against me. he/she said that i had sent him/her a very disturbing package in the mail that demoralized him/her, made a crude joke at his/her name, and gave a sarcastic message to him/her inside. he/she claiming that i did this cost me my job. is there any legal action i can take against this customer?