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Mr. Bolling had ruled he could not break ties on the budget.

Sen. A. Donald McEachin sued to block Mr. Bolling from using his tie-breaking vote to help Republicans organize the chamber, as Democrats did Tuesday. After a judge declined to intervene, the Henrico Democrat withdrew the lawsuit.

The Senate similarly was split 20-20 during the 1990s, and Donald S. Beyer Jr., the Democratic lieutenant governor, intended to use his tiebreaking vote in much the same way as Mr. Bolling. The plan was abandoned when Sen. Virgil H. Goode Jr. threatened to leave the Democratic Party if leaders refused to share power.