How Americaâs Vaccine System Makes People With Health Problems Fight for a Place in Line At least 37 states allow people with certain health conditions to receive the Covid-19 vaccine, according to a New York Times survey. But a new skirmish has emerged over who will go first. Waiting in line for Covid vaccines at a mass vaccination site in San Francisco.Credit...Jim Wilson/The New York Times Published March 9, 2021Updated March 27, 2021 As states have begun vaccinating Americans with medical conditions that may raise their risk for a severe case of Covid-19, they are setting widely varying rules about which conditions to prioritize.