OTTAWA—Canadian Prime Minister Justin Trudeau triggered the start of his campaign toward an Oct. 21 election, in which he will try to overcome damage from an ethics scandal and persuade voters to give the Liberal government another term based on the strength of its economic and environmental record.

Mr. Trudeau’s Liberal Party enters the campaign in a dead heat with its main rival, the Conservative Party, with support in the low-to-mid 30% range. The Liberal Party won its mandate in 2015 parliamentary elections with 40% of...