In New Jersey, Gov. Phil Murphy, a Democrat, said on Monday that residents 21 years of age and older who get at least one dose of a vaccine in May were eligible for a free beer if they show their vaccination card at one of several participating breweries. The program, introduced in conjunction with the Brewers Guild of New Jersey, naturally carries the moniker “a shot and a beer.” Connecticut has a similar program, in which residents who have received at least one dose of a vaccine can get a free beverage — alcoholic or nonalcoholic — at participating restaurants in the state for part of May. In Detroit, the city announced last week that it would offer $50 prepaid gift cards to anyone who drives a resident to select vaccination sites run by the city’s Health Department. There is no limit on how much people can earn driving Detroit residents to get vaccinated, but those who make $600 or more will have to fill out a W-9 form, city officials said.