56.5 for Montgomery and 70 for Butler County.
If we're looking at the same Ohio Department of Health report, page 9 has Montgomery County at 56.5 and Butler at 49.1
Of course, this is from 2005-2017, and there were marked changes in 2018.
In 2016, you'll find rates as high as 122.9/100,000 in Dayton zip codes. You can find that map at Montgomery County Environmental Public Health Tracking Portal.
As far as I know, that is the highest rate in the country at that point in time.
You can't really compare the 2017 Butler County Overdose Report to the 2018 Montgomery County Community Overdose Action Team report. Once again, there were massive differences between 2017 and 2018.
According to the Community Action Team report, page 3, Dayton with a population of 140,371 had 151 deaths from overdose in 2018.
According to the Middletown Division of Fire, Middletown with a population of 48,823 had 53 deaths from overdose in 2018.
If my math is right, that is a rate of 108.5/100,000 for Middletown and 107.5/100,000 for Dayton. This is also using 2018 Dayton population numbers, and 2017 Middletown population numbers. So based on 2018 Middletown population numbers, it could be higher or lower, but I can't find that data.
So the rates are nearly equal.
Bethesda North Hospital
Bethesda North Hospital isn't in Montgomery County.
It is in Montgomery, which is in Hamilton County.