On January 29, 2018, Murphy signed an executive order for New Jersey to rejoin the Regional Greenhouse Gas Initiative, which the state had withdrawn from under Gov. Chris Christie (R). The initiative—which at the time included Connecticut, Delaware, Maine, Maryland, Massachusetts, New Hampshire, New York, Rhode Island, and Vermont—capped how much carbon a plant powered by fossil fuels could emit. The initiative sought to reduce carbon dioxide emissions below 2005 levels. It was first formed in 2005 and initially joined by New Jersey. Christie signed an order removing the state in 2012.

On October 29, 2018, the state Legislature voted to establish a special commission (Legislative Select Oversight Committee) to investigate the hiring practices of Gov. Murphy's administration. The identical resolutions, SCR 148 and ACR 203, established a 15-member commission chaired by Senate Majority Leader Loretta Weinberg (D) and Assemblywoman Eliana Pintor Marin (D). The commission was created to look into the administration's hiring practices and stemmed from rape allegations against former staffer Albert J. Alvarez. On October 14, The Wall Street Journal reported that Katie Brennan, chief of staff to the New Jersey Housing and Mortgage Finance Agency, accused Alvarez of raping her after a campaign event in 2017. At that time, Brennan and Alvarez were volunteers for Murphy's gubernatorial campaign. Brennan said she told the administration about the allegations before Alvarez was hired as chief of staff to the Schools Development Authority. Alvarez resigned from his position October 2, 2018. Alvarez denied the accusations. The governor's office said Alvarez passed a background check before he was hired. The governor also launched his own investigation. The commission released its report on June 5, 2019. Its findings included a statement that Brennan's sexual harassment allegations against Alvarez should have been investigated before Alvarez was hired by Murphy's administration. "Upon learning of the sexual assault allegation made against Mr. Alvarez by someone working on a transition advisory committee, transition leadership should have immediately conducted a thorough and rigorous investigation into the allegation," the report stated. It also recommended changes to state laws and policies.

On Wednesday, February 10, 2021, Murphy announced he would enter a self-quarantine after a member of his family tested positive for COVID-19. Murphy and his wife, Tammy Murphy, began a self-quarantine on October 21, 2020, that was expected to go through October 25. Communications Director Mahen Gunaratna said in a statement that the governor and first lady received negative results after being tested for COVID-19 on October 21. Coronavirus pandemic Select a topic from the dropdown below to learn more.Political responses overviewState reopening plansDocumenting America's Path to RecoveryDaily updatesElection changesChanges to vote-by-mail and absentee voting proceduresFederal responsesState responsesState executive ordersStay-at-home ordersMultistate agreementsNon-governmental reopening plansEvictions and foreclosures policiesTravel restrictionsEnacted state legislationState legislative session changesSchool closuresState court closuresInmate releasesLocal government responsesDiagnosed or quarantined politiciansBallot measure changesArguments about government responsesThe 1918 influenza pandemicPandemic Response Accountability CommitteeUnemployment filingsLawsuitsSubmit COVID-19, also known as coronavirus disease 2019.