Can I relinquesh parental rights if child made claims of abuse and was unfounded?

Back in Nov of 2009 my 15 yr old daughter now 16 had made claims of ual abuse,the case was determined unfounded.Since this she conithues to slander my name to either people up here we know or to people down where she resides.My question is can a father relinquish his parental rights to a child if he feels the relationship will forever be severed due to her claims and continued threats of violence?