Can an official budget committee tell a governing body how to spend appropriated funds?

No. The budget committee's purpose is "to assist the voters in the prudent appropriation of funds" RSA 32:1. While the budget committee has a duty to review current expenditures, it is primarily for the preparation of future budgets, rather than to challenge or dispute what the governing body is doing. No one has legal authority to challenge the discretion of the governing body in making transfers among purposes of appropriation RSA 32:10 I. However if the bottom is overspent or expenditures are not properly entered and classified in municipal records, the budget committee has specific authority to petition the Superior Court for removal of the responsible official(s) under RSA 32:23.