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I'm a bit confused as an epidural and a urine test are different things. That said, if you're asking whether medicines routinely given for an epidural will show up on a urine test, the answer is "possibly." Though, if it did, it would likely show up as Cocaine (not morphine). Lidocaine is the most commonly used anasthetic used for an epidural and that is (distantly) related to Cocaine.
Hydrocodone, on the other hand, is a narcotic that is in the opiate family (like morphine). So, if the test is not specific, it could potentially show up as "morphine." And, since opiates tend to stay present (and therefore, detectable) in your system for a while, I wouldn't be surprised if this occurred.
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