Looks like you do not need to be a New York citizen to join the effort, though this is the closest I found to confirming it:
> Given that many employers are having many workers work from home, volunteers would collaborate virtually with New York State teams. So, preference will be given to those in the Eastern and Central US timezones but we are open to the west coast as well.
The interest submission form does not ask if you are a NYer, but does ask if you're willing to participate on-site or remote.
> A state official, who spoke on the condition of anonymity so he could talk candidly, told me New York needs help with digital tools directly related to the virus, such as building infrastructure for testing and scheduling. But officials also need to improve remote access to government services that could see a spike, such as unemployment services.
Volunteer program for individuals and organizations that can provide IT training, support or solutions for people who suddenly need to start working from home.
> Given that many employers are having many workers work from home, volunteers would collaborate virtually with New York State teams. So, preference will be given to those in the Eastern and Central US timezones but we are open to the west coast as well.
The interest submission form does not ask if you are a NYer, but does ask if you're willing to participate on-site or remote.