I get leak detection requests occasionally from prospective clients, most often in conjunction with a home they already own. I tell them leak detection is not an explicit part of a home inspection, though in the course of tracking down excess moisture accumulation leaks and their causes are sometimes obvious. The person is usually not interested in a home inspection, just someone who can detect leaks. But it raises an interesting question of how responsible a home inspector is for hunting down leaks.
To my knowledge, leak detection is not offered by any home inspector, even as a specialized service. I am aware of companies that detect leaks in swimming pools. And, of course, plumbers are well equipped to trace a pipe leak, and roofers a roof leak, back to its source. So there are experts in other fields that one can turn to. Still, though some practitioners of my trade expand their business by providing additional inspection services, such as radon testing, mold inspecting, or air pollutant sampling, there seems to be no inherent reason why leak detection couldn't be one of them.