Lamont made the announcement during a news conference Thursday but stressed that just because some businesses are allowed to be open does not mean people are required to go.
May 20 openings include outdoor areas of restaurants and bars, outdoor museums and zoos, offices and retail outlets. Barber shops, hair salons and other personal care businesses were types of businesses specifically mentioned.
Places that are "tough to socially distance" will take longer.
Casinos are "sensibly developing" a plan to socially distance and there are concerns about people coming from out of state could make that "a prime outbreak spot if we don't manage this very very carefully."
Employees are still urged to work from home when possible and face masks are still being encouraged as "an effective way" to prevent transmissions.
Re-openings for schools and public gatherings will be discussed by Lamont next week.
Lamont's plan relies on four levels - red, orange, yellow and green. The final level, green, may not be achieved for 10 months.
Lamont cited Georgia as an example for personal services businesses.
"Based on what we see in Georgia and other places, people aren't flooding in, people are doing it by appointment, so we are going to come up with some protocols that maybe give us an opportunity to get that started up on a limited basis starting on May 20," Lamont said.
People can make their own choices about whether to leave their homes, even after May 20.
But Lamont strongly recommends people older than 70 stay home.
So far there have been 2,257 reported deaths in the state and 27,700 positive cases.
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