Local case study
Meter first: the City's rules on who owns the leak
The City of Brighton's Distribution System Maintenance page explains that the City repairs the line up to and including the meter, and the owner is responsible from the hand valve to the house. It also gives a simple meter test for hidden leaks.
A water heater leak is on your side, but the meter test is a quick way to confirm that the heater is the only leak and not one of several.
