(1) The executive may sign or veto any ordinance or budget resolution adopted by the board of county commissioners. A veto by the executive may apply to all items or to any specific item of an ordinance or budget resolution appropriating money. Certification of a veto must be made by the executive within ten (10) days of the passage of the ordinance or budget resolution by the board of county commissioners. The board of county commissioners may override the veto by a two-thirds (2/3) vote of all its members called to a special session to consider the veto by a majority of its members.
(2) If the executive fails or refuses to sign any ordinance or budget resolution and return it with his written objections to the board of county commissioners within ten (10) days of the passage of the ordinance or resolution, it shall become law without his signature.