Other government accounts have also recently tried to take a more humorous approach. New York City’s Conflict of Interest Board has drawn on slang and memes, making the often dry conversation around government ethics more accessible. The city’s Police Department’s precincts have also tried a lighter tone and emojis to soften their public safety announcements.

Still, among states, New Jersey seems unusual for how successfully it has infused its online presence with such brashness.

Take Delaware’s account, @delaware_gov, with which New Jersey is in an ongoing Twitter feud. That state has taken a more staid approach to its social media and has about a third as many followers as @NJGov despite being about a decade older.

Perhaps no one message encapsulates New Jersey’s Twitter attitude better than “your mom”— a two-word tweet sent last December that vaulted @NJGov into the spotlight.

At the time, Ms. Gabel and Ms. Coyne had been running the Twitter account for months, mixing standard public-service announcements with their brand of Jersey humor. They had generated a modest following, to the extent that a curious internet user saw their tweets and questioned @NJGov’s reason for being. “Who let New Jersey have a Twitter,” he wrote.

Both women took umbrage.

“I was like, ‘That’s so rude,’” said Ms. Coyne. “And Pearl was like, I kind of want to respond, ‘your mom.’”

Ms. Coyne began laughing hysterically. Ms. Gabel, who sits in the cubicle next to her, took that as a good sign. After about 30 seconds of consideration, the pair sent the playground taunt to the online ether.