Is a dental hygienist allowed to sign the doctors RX for CHX with DR. approval?

No - dental hygienists in the United States are not legally allowed to sign a prescription for any drug, including chlorhexidine, even with the doctor''s permission. Signing your name or the doctor''s name could be interpreted as a violation of the prescribing laws under the state dental practice act. However, I believe that Oregon is the only exception, and is a state that allows dental hygienists to issue prescriptions for chlorhexidine. When in doubt, consult your state dental practice act and check under the regulations related to prescribing drugs.