Voters approved the 2012-13 budget Tuesday, despite the fact that all the taxes for the $81 million spending plan, which ended June 30, have been collected and all the money has been spent.

The vote was 1,534 to 1,029. Voters also approved setting the tax rate at 26.6 mills by a vote of 1,264 to 1,222.

On Monday, the finance office announced that a preliminary, unaudited review of the 2012-13 budget showed a $220,000 surplus.

Tuesday’s vote was the third time residents were asked to approve the city’s spending plan. The budget failed at two referendums, and the third petition for a referendum came so far into the fiscal year that the city attorney and the finance director said the outcome would be moot.

Revenues in the budget, which covered July 1, 2012, to June 30, 2013, were down by about $1 million, but it also included a $490,000 surplus in the $39.8 million education budget and a more than $300,000 surplus in the $41 million general government budget.