Yes, you can purchase a US property if you are a non-US resident. There are loan products available, but they will be a little costlier and you will have to put down a bigger down-payment. As your goal is to rent it out, you will need to buy a condo rather than a co-op. You do not necessarily need a management company to manage the apt. You can work out an agreement of how rent funds are transferred, and in the event repairs are needed, your tenant can get estimates for you if it is work beyond what the building staff can do. That is less costly than having just one unit professionally managed.
I suggest you use a skilled, experienced agent who has dealt with these situations before, as we know how to handle the intricacies of the situation and can guide you through the process. To find an agent, I would suggest you type in New York, NY in the search bar above and click "Find a Pro." Interview a couple of agents, make sure they have dealt with foreign investors before, and see who you click with.
Hope this helps.
Halstead Property, LLC