|Police responded to reports of gunfire at a home in Tyler, south-east of Dallas, at about 2pm on Monday.
Authorities identified the suspect as 24-year-old Tomas Wiggins Martinez, KLTV reports.
Both a man and woman were injured in the shooting, which police believe was a domestic incident.
Martinez is the father of the woman's child.
The man ran to a nearby restaurant after being shot, while police found the woman inside the home after following a blood
The shooting happened at a home on East Erwin and George Avenue.
The victims are both in hospital but the woman is in a critical condition.
Multiple officers were scouring the scene on Monday afternoon in search of the suspect.