should not affect your liver enzymes. The medication is metabolized in the liver, however it is not toxic to the liver. Zzzquil does not have acetaminophen
which is the one that most commonly can cause liver toxicity
Many other issues can alter your liver enzymes, and it depends on which enzymes were elevated and how high above the normal values.
Common causes of liver enzyme abnormality include (but not limited to): alcohol, fatty liver, hepatitis B, hepatitis C, certain medications, stones in the biliary tree, autoimmune liver disease. If your liver enzymes are persistently elevated you should discuss with your doctor
regarding further laboratory evaluation and depending upon results then an abdominal ultrasound.
Hope that helps.