She said the suspect fled with an accomplice in a car after the incident took place at around 8:30 am (1430 GMT).
"We are actively searching for them," Laney said, adding that the suspects had not been identified.
The courthouse and schools went into lockdown as police searched for the gunmen and their vehicle in Kaufman, a town with a population of only 7,000 in northern Texas. The courthouse was later closed.
The Dallas Morning News cited sources as saying that Hasse's caseload included investigations of members of the Aryan Brotherhood, though stressed that prosecuting attorneys typically handle nearly 400 cases at a time.
Unmarried, Hasse was survived by his mother and a brother.
"He was very well liked," Laney said.
In addition to the Texas Rangers, Kaufman County authorities are probing the shooting alongside federal agencies, including the Federal Bureau of Investigation and the Bureau of Alcohol, Tobacco, Firearms and Explosives.