Claudia Balducci holds a very slight lead over Girmay Zahilay in the race for King County executive, according to new public polling, but the contest is effectively tied as the two candidates politely fight for votes in the final week of the campaign to lead Washington’s largest county.

Balducci received the support of 37% of likely voters compared with 35% for Zahilay, according to the poll, the Civic Heartbeat Survey, conducted by the Northwest Progressive Institute. Another 28% of respondents said they were not sure how they would vote.

The results — the first public polling released in the race since the August primary — portray a race that could go either way as Election Day approaches.

They come as a modest surprise after Zahilay’s strong showing in the six-candidate primary, wher

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