The FDA approved a quick test for emergency use on April 2.
I doubt it was available immediately in hospitals, but it gives results in 15 minutes, Testing for immunoglobulin G and M. You can read the fact sheet here,
https://www.fda.gov/media/136623/download
I tried to find if there was any published data on this device but didn’t go deep. I’ll keep looking
IgG + IgM testing has been available through other manufacturers and seems to be valid for testing for active or recent infection when the virus has had time to produce an antibody response (4-10 days) It doesn’t differentiate whether it is current or recent or in the past.
More info here https://aytubio.com/covid-19/
The Cellex test is the only one currently approved by the FDA