WASHINGTON — Mayor Muriel Bowser is threatening residents of Washington, DC, with 90 days in jail and a $5,000 fine if they leave their homes during the coronavirus outbreak.

The threat of jail is alarming residents and civil libertarians who point out that at least five inmates tested positive for COVID-19 in the city’s 1,700-inmate jail near Capitol Hill.

“Our message remains the same: stay home,” Bowser, a Democrat, said in a statement Monday. The stay-home order has exceptions for grocery shopping and work deemed essential. Outdoor recreation such as running is allowed, but cannot involve people outside of a household.

The order is similar to dictates in neighboring Maryland and Virginia, but shocked residents of Washington, where there are just 401 of the nation’s 160,000 confirmed cases.

“This is insane. Criminal penalties?” tweeted Mercedes Schlapp, President Trump’s former White House director of strategic communications and an adviser to his re-election campaign.

Monica Hopkins, executive director of the ACLU of the District of Columbia, told The Post “we would be deeply concerned” if anyone actually was arrested for violating the order.

“When we saw this order, we thought, ‘You want to send them where?'” Hopkins said. “People being arrested for that causes all sorts of problems that are antithetical to the goals of lessening the virus.”

The ACLU of DC filed a lawsuit Monday seeking the appointment of an expert to help depopulate the city’s only jail of elderly, health-compromised and non-violent inmates. Many inmates are awaiting trial.

The labor union representing DC jail officers — a part of the Fraternal Order of Police — voted “no confidence” this month against Department of Corrections leaders over safety conditions to prevent spread of the virus.

Because DC courts are operating in a limited capacity due to the virus, it’s unclear when arrested people would be able to be released, Hopkins said.

“What we would hope for is voluntary compliance with the stay-at-home order and discretion on the part of officers to break those sort of things up and send people home,” Hopkins said.

DC’s Metropolitan Police Department did not immediately provide answers to The Post about enforcement, including whether residents would be issued warnings for a first offense. The city has a 6,500-person homeless population.

Trump said at a Monday evening press conference at the White House that federal officials are allowing local autonomy.

“We’re letting the governors do in their state pretty much what they want, with our supervision, and they consult with us in all cases,” Trump said.