US death rates per 100,000 from opioid overdoses 2016:
White 17.3
Black 10.5
Hispanic 6.1
Overall: 13.3
Asians are not reported in this data. There is a lot of variation by state.
For example, in New Mexico, the Hispanic death rate is 21.3, the highest in the country, but the white rate is below the national average at 15. There is not sufficient data on the black death rate. In West Virginia, the hardest hit state, the black death rate, 44.5, exceeds the white death rate, 46.5 (Hispanic NSD), while in another hard hit state, Connecticut the white rate is nearly double the national average at 30, the black death rate just above the average at 13.7, and the Hispanic death rate more than three times the average at 20.8.
DC has the highest black death rate in the country at 49.4, while the white death rate of 7.1, is considerably less than half the national white death rate. (Hispanic is NSD.) DC's overall death rate of 30 is fourth highest in the nation, after West Virginia, New Hampshire, and Ohio. Maryland and Massachusetts are close behind; both are 29.7.
https://www.kff.org/other/state-indicator/opioid-overdose-deaths-by-raceethnicity/?dataView=2¤tTimeframe=0&sortModel=%7B%22colId%22:%22Location%22,%22sort%22:%22asc%22%7D
State-by-state numbers hide high death rates in cities that are not in hard hit states. The top five counties with the highest death rates are those where the major cities are Pittsburgh, Philadelphia, Cleveland, Palm Beach, and Detroit (from highest to lowest), even though overall Pennsylvania, Florida, and Michigan have overall death rates that are just above the national overall rate.
https://www.pewtrusts.org/en/research-and-analysis/articles/2018/02/15/philadelphias-drug-overdose-death-rate-among-highest-in-nation
Reliable global figures are very hard to find. Canada seems to be behind the US, Scotland likely has the highest death rate in Europe, but numbers are very unreliable for Asia and elsewhere. There are arguments the US opioid crisis is going global as seen in articles likes this one in a recent issue of Foreign Affairs:
"This public health story [the U.S. opioid crisis] is now common knowledge. Less well known is the growing risk that the epidemic will spread across the globe. Facing a backlash in the United States and Canada, drug companies are turning their attention to Asia and Europe and repeating the tactics that created the crisis in the first place. At the same time, the rise of fentanyl, a highly potent synthetic opioid, has made the outbreak even deadlier and begun to reshape the global drug market, a development with significant foreign policy implications. As a result, the world is on the cusp of a global opioid epidemic, driven by the overuse of legal painkillers and worsened by the spread of fentanyl, that could mark a public health disaster of historic proportions."
https://www.foreignaffairs.com/articles/world/2018-04-16/opioids-masses