Do I need a permit to burn Brush?

Yes, unless there is sufficient snow cover. See the Outdoor Burning Policy for more information on when permits are required, and how to obtain one.

It's the LAW - RSA 227-L:17(II)
Anyone who wishes to burn clean, ordinary combustibles such as leaves, brush or untreated lumber, or have a camp or cooking fire must have written permission from the landowner and a fire permit from the fire department.