The suspect is believed to be dead and the threat is believed to be over, they said.
Officers were fired at as they approached, and one officer pulled the Dallas paramedic out of harm's way, placing him in his squad car and driving him to the hospital yesterday, officials said.
A robot was sent into a home, where it located two deceased people, including the individual whom authorities believe was the shooter, police said.
While no identities have been confirmed, authorities feel confident that the suspect was dead inside the home.
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Several streets were closed and people residents were urged to avoid the area after the first incident at 11.30 AM (local time).
"Dallas Fire and Rescue arrived on the scene where a civilian had been shot and immediately began treatment. During this time, the suspect approached the area and then opened fire. A EMT paramedic was wounded, a Dallas Police Department statement said.
"Dallas Police Department is searching for the suspect who they believe is still in the vicinity," it said.
The city issued an emergency alert after the incident.
"This remains an active scene and we will provide additional information as it becomes available," it said.