Ttgjyuk

In law enforcement (and the judicial system in general in the U.S.) nearly every legal process has a Latin term. Although, one has escaped us and our legal staff. Our agency is looking for a Latin term that would best describe a Search Warrant for Digital/Virtual Data maintained in another state (location that is). A term that encompasses what is obviously not tangible like paper or articles — but, well, virtual...

In other words I'm looking for something that means, "an order (from a court) to search and deliver intangible electronic (digital) information stored on a computer far way".

Any suggestions?

I'm not aware of a Latin word for a "search warrant" in general, but an "arrest warrant" is known as a capias: literally, "you should seize [this person]". In Latin it's a verb, but it's used as a noun in English, like with habeas corpus ("you should have the body"): officially it's probably something like "a writ of capias".

So perhaps we could call a search warrant an inquiras, "you should search for damning evidence". (The verb inquiro means to search for something in general, but it was also a legal term, when a prosecutor searched for evidence against the defendant.)

The "virtual" part is a bit harder, since the Romans didn't have computer files. Virtualia are literally "virtual things", or you could go with electronica, "electronic things"; neither would make sense in an ancient Roman or mediaeval European court, but I don't think the concept would either. For an English-speaking audience you could even use data, but in Latin that's literally "the things that have been handed over", which is totally different in a legal context—if you're carrying out a search warrant, the user probably isn't "handing over" anything willingly.

Whichever noun you choose, I'd put it after the verb, on the model of habeas corpus. So your warrant might be, perhaps, "a writ of inquiras virtualia".