Wow, that is a pretty big city — with a population of more than 277,000 — to not have its own emergency management function organic to the city.
As a former county emergency manager, I understand how there is a need for regional coordination between cities in a county, and maybe you could have a “combined emergency office.” (I once proposed looking into that with the city of Seattle — there was no interest).
This article, “Another Voice: Buffalo needs an emergency management office,” calls the issue into question. That decision is up to the city’s fathers, but there is nothing like a major disaster with many deaths to bring attention to how emergency management functions or is supported by the city and the county.