Millions of dollars are flowing into the tight congressional race for Southwest Washington’s swing 3rd Congressional District, bolstering campaigns to reelect U.S. Rep. Marie Gluesenkamp Perez or flip the seat for state Sen. John Braun. Much of that money comes from outside Washington, according to Federal Election Commission filings.

About half of the donors who have contributed more than $200 to either candidate’s campaign are from Washington state; the rest are from elsewhere in the country, federal filings show as of mid-October. Meanwhile, outside groups have poured more than $18 million into the district to influence voters through advertisements, texts, phone calls, emails and other outreach.

The vast influx of funds from beyond the state underscore the race’s national stakes. The 3rd District has produced a string of close congressional contests in recent years and is one of few races nationwide that may help determine which party controls the U.S. House.…