Well you can certainly make that argument. The problem is that you'll be sitting in jail while an appeals court decides whether or not you have a legitimate argument. While your on probation, your rights are lessened, and probation probably has the right to ask for proof of the prescriptions. As I said, you can prove your innocence from jail, but why if you can avoid the hassle now. I say if you got the prescriptions, show them.
You should comply with your probation officer's request.
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I would do it. The reason is this; if you test positive for a controlled substance you want to make sure the PO knows that you are prescribed it. Why do you not want to show the PO?
In reading your question, I would first tell you to follow all of the general and specific rules of your probation, specifically in reference to prescription drugs.
Generally this is an issue related to drug offender probation, or probation where drugs/alcohol may have been involved in your case. If so, this is generally a legitimate request. If not, you MAY have a legitimate claim that there is no nexus between your crime/probation and the probation officer's need to know about your prescriptions. That would be an area where I would suggest you may want to speak with a good criminal defense lawyer in your area.
There are a plenty of reasons that the probation officer may want to see your prescription records, including (but not limited to):
1) You are being (or are to be) drug tested, and they want to know what drugs you legally have under prescription;
2) They may be concerned that you are doctor shopping to get multiple medications; or are committing prescription fraud;
3) You live with someone else on probation who should not have access to these medications;
Geoffrey R. Mason