As the bear approached, Kelly made herself as tall as she could, then punched it, the department said. The bear responded by biting her in the right hand and then fleeing. She suffered a punctured wrist and was treated at Memorial Hospital in North Conway, N.H.

In the second incident, on Saturday morning, a 65-year-old man in Litchfield, Conn., suffered injuries that weren’t life-threatening after he tried to stop a bear from attacking his dog, said Paul Copleman, a spokesman for the Connecticut Department of Energy and Environmental Protection. Copleman did not mention the man’s name.

The bear wandered onto the man’s property, attracted by his bird feeders, and his dog chased it, prompting the attack, Copleman said. Afterward, the bear fled into the woods, he added.

Authorities in both states were still searching for the bears.

Connecticut has seen a rise in “human-bear conflicts” in recent years, prompting lawmakers to pass legislation allowing people to kill “bears that cause harm to a person or pet or that enter an occupied building.”

Experts say unprovoked bear attacks are rare. Wildlife authorities say that dog owners should walk their pets on a short leash that doesn’t retract, and that people should remove all sources of food, including bird feeders or bird seed, from outdoor spaces because they can attract bears.

What should I do if I see a bear? First, don’t run away.

Speaking to 7 News, Kelly said that the bear in Maine “just kept coming closer, so I had to fight him off because I wasn’t going to run from him because I know they’ll catch you.”

The bear was “a foot taller than I was and coming at me,” she said. “Then he stood up and I tried to make myself as big as I could and was screaming and yelling.”

According to the National Park Service, if you surprise a bear and it is not acting in a predatory way toward you, you should wave your arms to show the bear that you are human and then “slowly and calmly back away while avoiding direct eye contact.”

However, if a black bear charges or attacks, the Park Service’s advice is to “fight back with everything you have.” (It’s good to know what kind of bears live in your area, though, because the advice for grizzly bears is the opposite: “Play dead. Do not fight back,” the Park Service says.)

Wildlife experts previously told The Washington Post that if you are forced to confront a bear, you should focus your blows on its face. You should not run away because the bear could see you as prey — and it can outrun you.

Mark Latti, a spokesman for the Maine Department of Inland Fisheries and Wildlife, told 7 News that although the state has a lot of black bears, they don’t typically attack people. “Usually, it’s in response to something else. In this case, it was in response to being punched in the nose,” he said.

The rule is to not run away from a bear. This professional runner did just that.

The Connecticut Department of Energy and Environmental Protection recommends that people “take down, clean, and put away bird feeders by late March, or even earlier during mild weather,” to avoid bears. Bird seed and feeders can attract bears, even when they are hung on porches protected by screens or stored indoors behind windows, it said. The best place to store these items is “in a location not accessible to bears, such as a closed garage.”

According to the agency, “bears looking for human food and garbage can damage property and injure people.” Anyone living near bears should carefully clean and store any source of food, it said.

The warning is relevant ahead of the July Fourth holiday, when many people have outdoor barbecues. The agency recommends that people keep their grills clean and store them indoors and “store garbage in secure, airtight containers inside a garage or other enclosed storage area.”

Teddy Amenabar contributed to this report.