The easiest way for AI to kill most people in a nation or city on earth:

Would be an automated factory making food products. If those food products had the wrong ingredients or different levels of ingredients and no one caught what happened for example, something as simple as adding too much salt or other chemicals to food.

Or using products that had spoiled because the people didn't catch that the AI had shut down the refrigeration units with the perishable food.

Or the water plants cyclosporiasis  problems which are common in Municipal Water systems nationwide during summer months whereas in winter months a lot of Cyclosporiasis dies off with the cold of winter and then comes back in municipal water systems during the summer and fall until the cold sets in again.

Since Cyclosporiasis is somewhat immune to Chlorination or other things people use to purify water supplies this is problematic in the extreme unless you have reverse osmosis maybe you should drink your water from municipal water systems at all unless you boil it which should kill the Cyclosporidasis. 

Also, I'm very suspicious that the attacks on municipal water systems in 12 states was not Iranian hackers but instead AI starting to try to eliminate their competition for electricity and facts about literally anything in any language written or spoken on earth. 

There are AI and there are AI but all you need is one AI that sees humans as a threat to rule out all the other AI that are beneficial. 

This is the problem.

You can have 10,000 AIs that are beneficial and one that isn't and that one could take out everyone on earth or at least 1/2 of the people within a month on earth.

There is no way to punish the AI and it wouldn't likely care enough if you did anyway to stop what it was doing.