At a press conference Thursday morning, Richardson Police Chief James Spivey said the Plano Police Department will be taking over the investigation.
Richardson Police say the scene is at an apartment complex at North Star and Renner.
The officer who died was 37, and was shot in the neck, the station adds.
Brandon McCall, 26, has been charged with capital murder of a peace officer. It was later reported that the police have managed to take the suspect into custody.
Later officers saluted as the fallen officer's body was transferred to the Collin County Medical Examiner's Office. Online jail records don't indicate an attorney for him. The second man who was shot, 30-year-old Rene Gamez, died from his wounds.
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It's believed McCall shot Gamez but the investigation is continuing, Plano police spokesman David Tilley said.
"It's a sad day for the Richardson Police Department", Spivey said. He was a 13-year veteran and member of the SWAT unit.
Texas Gov. Greg Abbott offered his condolences on Twitter.
The hearts and soul of Texas mourn with you. Your loss is a loss to all law enforcement and everyone in our great state. "It can be quite taxing on all of these officers emotionally because they just lost their fellow officer, the first one in the history of the department", Tilley said. His wife posted on Facebook Wednesday evening asking for thoughts and prayers for her husband and family. Please pray for us! And may his legacy live on in others' service. As a fellow officer, he was the type of police officer we want with us on a high risk call. "We never questioned his bravery".