I seriously doubt that it is standard operating procedures anywhere in the country.
Rather, weapons carried by officers nearly always must be either issued by the department, or registered with the department. Some, or perhaps, many departments simply do not allow officers to carry personally owned weapons. A department that permits officers to carry their own weapons may have restrictions in addition to registering the weapon with the department (must be of a certain design, caliber, or even from a selection of certain models).
Though say, a rural department can have relaxed rules about personally owned weapons and allow officers to carry what they want with in reason, many officer would probably shy away from borrowing weapons. Their life can depend on that weapon. Thus officers want to carry a weapon that they are totally familiar with in grip, weight, trigger pull, safeties or the lack there of, maintenance etc.
In the end, I don't think officer routinely carry borrowed weapons for a variety of reasons.
I think many cannot understand the level of police corruption that there is in small Ohio towns/counties. I saw it up close in Illinois and now in Ohio. I see it everyday.
How about this cop that just got only 2 years for dealing drugs next to a school? This town is about 30 mins from me.
Ex-state trooper sentenced to 2 years for being part of drug-trafficking ring
How about this one? This guy was faking time cards for himself and other officers, taking petty cash, stealing cash from dead bodies etc etc. When I commented on Facebook he (and his friends) went after me. Oddly he had many people that wanted him to keep his job. I used to sell real estate in this town. Its about 15 mins from where I live now. The Chief before this one was as bad or worse.
Buckeye Lake Council votes to dismiss police chief