This is False. The federal government does not allow citizens to decide how public money is used.
When citizens have this power it is called Real budget democracy. Now the budget is decided by the Congress passing through many stages. First the Departments and agencies bring on proposals to the White House for the creation of the President's budget, then the House of representatives and Senate make their resolutions and a final budget is created that must be approved for the next fiscal year, that is voted, passed and signed as law.