The pandemic is ebbing, but what about governors’ emergency powers?

As the threat from the coronavirus pandemic grew in early 2020, so did many governors’ executive powers. Without a federal plan, it fell to the states to issue lockdown and stay-at-home orders, mandate masks, and close schools and businesses.

Nearly 14 months later, with states moving to reopen amid a drastic drop in new cases, legislators have been asking about the current need for restrictions, and just how much sweeping authority governors need to have during a public health emergency.

Voters in Pennsylvania this week became the first in the United States to help check an executive’s authority during an emergency period. The state’s Democratic governor, Tom Wolf, and its Republican-controlled legislature sparred over Mr. Wolf’s emergency actions, which included closing schools and many businesses, during the pandemic.

Two measures passed on Tuesday in Pennsylvania, both with about 54 percent approval. The state’s Constitution will be amended to end a governor’s emergency disaster declaration after 21 days. And lawmakers, with a simple majority, will be given the only authority to extend or end the emergency disaster declaration. The ballot questions had been pushed forward by Republican legislators.

At polling stations, many voters told Pennsylvania news outlets that they had been driven to vote in particular because of the ballot questions on executive power. Previously, a governor could issue a declaration for up to 90 days and extend it indefinitely and the legislature would need a two-thirds majority to stop a declaration. Mr. Wolf’s first 90-day virus emergency went into effect in March 2020, and his latest extension ends this week. But all of the remaining capacity restrictions on businesses and social gatherings in Pennsylvania end on May 31.

“We had a long period to see how the current system works, and there was some thought that we could do better,” Mr. Wolf said this week. “So I’m looking forward to working with the legislature to figure out how to make this work.”

In New Jersey, a Democratic-led legislature took the initial step this week to roll back dozens of Covid-related orders issued by Gov. Philip D. Murphy, also a Democrat. But the bill that was introduced also leaves the governor with expansive powers to apply new measures in an emergency. Mr. Murphy is one of two governors to keep an indoor mask mandate, even for vaccinated people; the other is Hawaii’s.

New executive orders related to the pandemic are still being announced. Gov. Greg Abbott of Texas, a Republican, said on Tuesday that counties, cities, public health authorities and local government officials in his state would be prohibited from requiring people to wear masks. His order came days after federal health officials announced new guidance that encouraged people who were fully vaccinated to forgo masks in most situations.

Democratic lawmakers in Connecticut, though, supported an extension this week of Gov. Ned Lamont’s expanded pandemic powers through mid-July. They were set to expire this week. Lawmakers argued that executive orders were still needed to manage the vaccine rollout and federal relief funds.

But perhaps no governor more than Andrew M. Cuomo, Democrat of New York, has faced a bigger rebuke in his use of emergency powers by a Democratic-controlled legislature. In March, the body curtailed Mr. Cuomo’s emergency powers, and in late April, it suspended some of his pandemic directives, including a rule that required New Yorkers to order food with their alcohol orders at bars and restaurants.

Mr. Cuomo also faces federal and state investigations, including one looking into his reporting of deaths at nursing homes during the pandemic.