A woman continues to fight for her life in a Minneapolis hospital after she drove herself and her toddler son to the hospital when both were severely wounded by gunfire.

A spokeswoman for HCMC said late Tuesday afternoon that Lilian M. Polacin Perez, 35, of Minneapolis remains in critical condition after she and her 2-year-old were shot Sunday night while in a vehicle in an alley in the 2900 block of 18th Avenue S.

Polacin Perez drove herself and her son about 1ΒΌ miles to Children's Minnesota-Minneapolis while both were suffering from "potentially life-threatening gunshot wounds," a police statement read. Polacin Perez was later transferred to HCMC.

In a statement, Police Chief Brian O'Hara called the shooting of a child "absolutely horrific. It is outrageous. I am most thankful that it appears this child will survive."

Polacin Perez's brother-in-law, Jamie Chachipanta, told the Star Tribune that the boy is named Suriel, and "I think he is going to be OK. That is what the doctors said."

Police said a male dressed in dark clothing shot the woman and her toddler. The gunfire hit the child in the face, police said.

"MPD is investigating the sequence of events that led up to the shooting and is working to determine if this was a targeted shooting," the police statement read.

There have been no arrests as of late Tuesday morning, police said.

Police also said they have not yet made an arrest in a shooting about 20 minutes later and a few blocks away at a house in the 2800 block of 16th Avenue S.

A 32-year-old man had been shot and was taken to HCMC. Preliminary information indicated the victim and the shooter knew each other, police said. The victim's identity has yet to be released.

A search warrant affidavit filed Monday in Hennepin County District Court disclosed that the man was in critical condition after a being shot in the throat while he was in a first-floor bedroom.

Witnesses told police that the man arrived at the home with a woman and two men, according to the filing. After the gunfire, the woman and the two men fled the home.

After a judge read the affidavit and allowed police to search the home, investigators recovered two live rounds of ammunition, a $1 bill rolled up and containing "unknown contents," five cellphones, drug paraphernalia and one discharged cartridge casing.