Can a home inspector determine if a home is hooked up to city sewer?

Not from just the home inspection, You will have to check with the city or company that does the sewer lines and see if that location was hooked up or not. From crawl space or basement, you merely see the sewer line going out of the house. At some locations a septic clean out would be visible.

This also has to be disclosed by the seller. And should be on the listing agreement, you can require that to be verified if you wish.