LORAIN, Ohio — Welcome to Lorain, where the mayor, Chase Ritenauer, would like to show you around.

The police car over there? It broke down during a pursuit not long ago, leaving the officer to continue the chase on foot. The new high school? It is part of a school system so badly underfunded that it is now overseen by the state. Traffic signals are kept operating with parts recycled from discarded traffic lights.

This city of 63,000 is in such dire financial straits that it has ceded part of an administrative building to raccoons; repeatedly calling the exterminator was too costly.

But even as Lorain and many other Ohio cities are barely scraping by, the state government is flush with money.

Ohio announced a budget surplus of $657 million in July. State officials have made it clear, however, that none of the windfall will go to Lorain or any other city or town, many of which are struggling because of heavy cuts made by the state over the years.