Three police vehicles and one belonging to the circle officer were damaged by protesters in Mashrakh block, where the school is located, Saran Superintendent of Police Sujit Kumar said.
In the district headquarters at Chapra the protesters targeted a police bus used for carrying prisoners and broke its glasses. They also damaged one police checkpost, official sources said.
The day-long Saran bandh call has been given separately by three parties - RJD, BJP and LJP.
Though schools, colleges, banks and government offices are open, thin attendance was recorded in all the institutions.
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Policemen wielded lathis at some places in Chapra to quell stone pelting protesters, the sources said.
Workers of the three parties are moving around in Chapra and other parts of the district to impose bandh.
RJD protesters are being led by newly elected MP from Maharajganj, Prabhunath Singh. Chapra is the Lok Sabha constituency of party president Lalu Prasad.
Prasad had visited the ailing children admitted at PMCH in the state capital.