The first SARS-CoV-2 home diagnostic test was approved on April 21, 2020. The test was developed by Labcorp. The initial plans are to make the test available to healthcare workers.
The test however, can not be used in states such as Maryland, New Jersey, New York, or Rhode Island because those states currently only allow tests to be administered by physicians.
Kaiser Family Health News reports the story in detail here https://www.kff.org/coronavirus-policy-watch/at-home-sars-cov-2-diagnostic-tests-could-be-a-breakthrough-but-what-are-the-limitations/.