GOV. CHARLIE BAKER on Saturday declined to say whether the state will begin reopening on May 4, but he didn’t rule it out.

On a visit to a Cartamundi/Hasbro manufacturing facility in East Longmeadow that has started making medical face shields, the governor was more specific than usual about what would be needed to begin the reopening process.

“Any decisions we make with respect to reopening are going to require two things,” he said. “Number one, the same thing required almost everywhere else, which is some drop in hospitalization rates and some evidence that we are in fact over the hump with respect to the surge. The second is putting rules for engagement or reopening in place, which we’ll have a lot more to say about next week.”

The state’s COVID-19 dashboard reported on Sunday that hospitalizations, after three days of declines, were up 32 to 3,879. Fifty-five percent of the state’s hospital beds are empty.

Baker on Saturday said the state is in the midst of the COVID-19 surge, but there were some signs that the rise in cases may be slowing. After record-high increases on Thursday and Friday,  the number of new cases fell to 2,379 on Saturday and 1,590 on Sunday. Deaths also continue to rise, increasing by 169 on Sunday for a total of 2,899. Deaths at long-term care facilities rose the fastest; they accounted for nearly two-thirds of the new deaths on Sunday and 56 percent of all deaths.

Baker’s emergency order advising people to remain at home and barring non-essential businesses from opening is set to expire May 4. Baker on Saturday again stressed that the May 4 date is not what people should be focusing on. He has said over the last few days that his administration is preparing rules of the road for when the state reopens. He has indicated a company’s ability to abide by those rules would determine whether it can open or not.

Baker said he would talk a lot more about the rules of the road next week, an indication they are coming. “Whatever the rules of the road look like for reopening, masks and face coverings are going to be a big part of it,” he said.

At a press conference after Baker, Lt. Gov. Karyn Polito, and US Rep. Richard Neal toured the Hasbro facility, Neal said he is already working on another COVID-19 relief bill. President Trump on Friday signed the latest $484 billion stimulus package.

Neal, the chair of the House Ways and Means Committee, said the next bill will provide money for unemployment insurance benefits, state and municipal governments, and possibly more checks for most Americans. He said the bill should be ready in 10 days, but Senate Republicans have raised questions about additional government spending.