Law Enforcement Looking For 57-Year-Old Man in Connection to Minnesota Shootings

Police are looking for a 57-year-old man in connection to the shootings that left a Democratic lawmaker and her husband dead, and another politician and his wife hospitalized, TMZ can confirm.

Vance Luther Boelter is being sought, a source familiar with the investigation tells TMZ. Authorities released a picture of Boelter wearing a big cowboy hat they say was taken this morning at a business in the Twin Cities area.

As you know ... Representative Melissa Hortman and Senator John Hoffman -- both members of the Minnesota State Legislature -- were shot early Saturday morning.

According to officials ... a man dressed as a police officer, driving an SUV that had the appearance of a squad car, showed up to Hortman's home. He then shot and killed Hortman and her husband.

Officers say they exchanged gunfire with the suspect at Hortman's house before he escaped on foot.

We shared the dispatch audio from Hoffman's shooting ... and, the first responders detailed his injuries -- revealing the state senator was shot twice in the chest and once in the abdomen.

CNN reports the bullets narrowly missed Hoffman's heart ... while his wife, Yvette, saved their daughter's life by jumping on top of her to protect her.

A manifesto allegedly written by the suspected shooter was recovered, according to officials ... which listed numerous others that are believed to be targets.

Senate Minority Leader Chuck Schumer has asked Capitol Police for more protection for Senators Amy Klobuchar and Tina Smith from Minnesota.