The school district in Dallas has drawn backlash from parents after giving elementary school students a Winnie the Pooh-themed book that teaches children how to “run, hide, fight” in dangerous situations like a mass shooting.

Cindy Campos, whose two children attend an elementary school in the Dallas Independent School District, said that she wasn’t sure what to do when her youngest son, who is in prekindergarten, came home from school last week with the book, titled “Stay Safe.”

The book, Ms. Campos said, had been tucked into her son’s backpack with no note or instructions.

“If danger is near, do not fear,” the book reads. “Hide like Pooh does until the police appear.”

At first, Ms. Campos said that she wondered if it was a gift from her son’s teacher. But later that evening, she found the same book in the backpack of her older son, a first grader. That’s when she said she started to wonder whether the book was an initiative from the school district.

“The book was not something I wanted,” Ms. Campos said. “It’s unsolicited advice.”

Other parents also complained, wondering why the book was given out without instruction and calling the distribution “tone deaf” for being shared so close to the anniversary of a mass shooting at an elementary school in Uvalde, Texas, where 19 students and two teachers were killed.

The distribution of the book also came about a week after a gunman shot and killed eight people, including three children, at an outdoor mall on May 6 in Allen, Texas, a suburb north of Dallas.

“After you read a book to them, they have like 50 questions,” Ms. Campos said. “How do you go to bed letting them know, ‘Yeah, this is what you do if you get shot up at school,’ and then let them go to sleep?”

“That’s a nightmare waiting to happen,” she said.

The book also drew the attention of Gov. Gavin Newsom of California, who said on Twitter on Tuesday that “Winnie the Pooh is now teaching Texas kids about active shooters because the elected officials do not have the courage to keep our kids safe and pass common sense gun safety laws.”

In a statement on Friday, the school district said that the book was sent home “so parents could discuss with their children how to stay safe” in dangerous situations at schools, such as a shooting. Still, the district conceded that it should have given parents guidance about the book.

“We work every day to prevent school shootings by dealing with online threats and by hardening our schools,” the district said in an email. “Recently a booklet was sent home so parents could discuss with their children how to stay safe in such cases. Unfortunately, we did not provide parents any guide or context. We apologize for the confusion and are thankful to parents who reached out to assist us in being better partners.”

The district did not disclose how many books were distributed or which schools and grades received them.

The Texas Education Agency, which oversees schools across the state, said on Friday that the book was not part of an agencywide initiative, and deferred questions about the book to the Dallas school district.

Ms. Campos said that the book has not been addressed by the school’s principal or its teachers. The school’s principal did not respond to a request for comment on Friday.

The book is published by Praetorian Consulting, a Houston-based firm that provides safety, security, and crisis management training and services. It did not respond to requests for comment on Friday.

The book, which was written by Ken Adcox, the owner of Praetorian, and Brittany Adcox-Flores, does not explicitly mention guns. Instead, it refers to threats as “danger” and “something that is not right.”

Mr. Adcox did not immediately respond to a request for comment on Friday, and Ms. Adcox-Flores could not immediately be reached.

The “Stay Safe” book was created by Texas police officers and teachers to teach elementary school students how to “remain safe and protect themselves should a dangerous school intrusion take place,” Praetorian said on its website.

The company said that the material, which features “the well-known and beloved characters” of Winnie the Pooh, teaches the “run, hide, fight” response, which is recommend in an active shooter situation by the Federal Bureau of Investigation and the U.S. Department of Homeland Security.

Winnie the Pooh, which was originally published in 1926, entered the public domain last year, allowing for adaptations of its characters.

“It is our belief,” Praetorian said, “that as with other school safety strategies like fire drills, pedestrian safety and stranger-danger, the concepts of Run, Hide, Fight must be discussed regularly with students of all ages.”

The National Association of School Psychologists recommends that parents and teachers who talk to elementary school children about violence should give “brief, simple information that should be balanced with reassurances that their school and homes are safe and that adults are there to protect them,” according to guidance from the organization.

Parents and teachers should remind young children of examples of safety, such as locked doors, the organization said in guidance on its website. The National Association of School Psychologists did not respond to a request for comment about the Winnie the Pooh book.

Ms. Campos said that the school district’s distribution of the book felt like an attempt to “normalize” a wave of gun violence across the country.

“It’s heartbreaking,” Ms. Campos said of having to talk to her children about gun violence. “We shouldn’t have to talk to them about it, and it’s so hard as a parent.”

Eventually, Ms. Campos said, she relented and read the book her youngest son, who is 5.

“There was no way he was not going to let me read it,” Ms. Campos said, adding that her son was interested because of Winnie the Pooh.

“I’m finishing the book crying, and he’s like, ‘Why are you crying?’”