Well, the world standard kilogram is in France. The US has a copy. Every once in a while it is (or used to be) transported to France to be compared against the original. I have a lot of friends who work at NIST, and they talk about the lengths and paperwork the people who transport it have to go through when explaining to TSA that, no, under no circumstances can they open, inspect or be separated from the kilogram.
About a year ago the kilogram was internationally redefined in terms of physical constants, so the international and national kilograms are now just historical artifacts and conveniences. This was in part motivated by the fact that even in their extremely careful storage conditions, the international kilogram was changing, and had changed in mass by 50 parts per billion in the last ~100 years. The standard meter was officially retired decades ago.
But I assume the NIST police are more concerned with investigating weights and measures fraud and enforcing traceable calibration for measurements used in commerce. After all, ultimately one big part of their job is making sure that when you buy 5 lb of flour or 1 gallon of gas you get the right amount.
Generally state departments of weights and measures Although they might also be the people who provide physical security at NIST facilities.