(CNN) -- The mother of Rebecca Sedwick, a Florida girl who jumped to her death after being bullied by classmates, on Tuesday urged parents of potential victims to pay attention to the signs of bullying.
"When I looked at my child I saw a normal, happy, productive child," Tricia Norman told CNN's Chris Cuomo on "New Day." "Apparently not. Inside, behind the scenes, there were other things going on with the bullying. Even though your child may seem normal, there may be something else going on."
The interview comes one day after Norman and her lawyer announced plans to sue those they believe responsible for the 12-year-old's suicide. Authorities last week dropped criminal charges against two girls accused of cyberbullying Rebecca Sedwick.
The civil wrongful death lawsuit has not yet been filed, and Norman did not specify the targets of the future legal action.
In addition, Norman's attorney, Matt Morgan, is pushing Florida lawmakers to enact "Rebecca's Law" -- legislation that would allow the state to file bullying charges against minors and their parents, and make parents liable in civil court.
"For the parent, I think civil responsibility," Morgan told New Day on Tuesday. "If parents know they can be held financially responsible for the acts of their children then ultimately that might provide a deterring effect for them to monitor their child's behavior."
Rebecca, 12, died after jumping from the top of an abandoned concrete plant in September.
Norman said all her efforts to halt the bullying -- including counseling, reporting the harassment to school officials as well as other parents, even removing her daughter from school -- failed to deter the alleged bullies.
"It just wouldn't stop," she said, "no matter what we did to try to eliminate it."
Norman said the abuse was unrelenting and had nothing to do with her daughter not having "thick skin."
"I think her skin was thick enough," she said. "I think (the bullying) was so much and so often."
Authorities said Rebecca killed herself after months of cyberbullying from fellow students. The abusive behavior that authorities say prompted her suicide grew from a dispute between Rebecca and a former classmate over a boy they had both dated, police said in October.
Authorities initially charged two girls, ages 12 and 14, with aggravated stalking, but the charges were dropped last week.
The state attorney's office declined to comment about the dropped charges and referred CNN to the girls' defense lawyers, who praised the decision and said there was no evidence of stalking.
Police said the abuse included messages such as "nobody cares about u," "i hate u," and "you seriously deserve to die."
Rebecca had already cut open her wrists months before the jump, but survived that suicide attempt.
"I think people should know what was done to my daughter," Norman said Tuesday.
She said parents need to take the signs of bullying seriously.
"If your child is being bullied, don't ever give up -- don't ever think it just went away."