Even big police forces, e.g. NYPD, have lots of divisions. I don't think there's any standard operating procedure in place that would lead a random detective in a random precinct to call in one of the two or three experts across the entire NYPD on a case he is working that happens to involve seizure order for servers. If someone in the special city-wide child pornography unit was involved in a server seizure, that's when the computer expert might be involved (because he or she would be attached to the computer crimes division the child porn unit is a part of).
If they were the first to respond to a tech crime, they could probably create a mess. But in theory, they could do their own search warrants, searches, recommending prosecutions, etc.