Can I sign over my parental rights in the state of Utah if I feel Im an unfit parent?

Depends. First, you cannot just sign them over. This is because the child has certain rights and you have certain obligations that would be extinguished if you were allowed to do this. For instance, you have an obligation to support the child and, unless, someone is willing to fulfill this need, such as adoption, it will not be in the child's "best interest" to let you off the hook. However, if another party/parent wants to terminate your parental right and files the appropriate paperwork, you could stipulate to your rights being terminated. Hope this helps.