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Her daughter will start hitting and punching, attacking the dog, throwing things across the room, sending her 5-year-old brother into a corner to hide.

Ms. Gallagher, on behalf of the Campaign for Children’s Mental Health, requested that the General Assembly fund five pilot programs of crisis-response services for children — one for each of five regions across the state — so they can avoid hospitalization.

Delegate Kenneth R. Plum, Fairfax Democrat, one of the handful of legislators at the hearing, said the state had placed an increased emphasis on mental health after the Virginia Tech tragedy in 2007, in which Seung-Hui Cho, who had a long history of such issues, killed 32 people in Blacksburg before committing suicide. Funding waned, however, as the recession took hold.

“It’s not a new problem,” Mr. Plum said. “We’ve been behind. We raised expectations that I think were justifiably expected, but we haven’t been able to” follow through.