DPS said Wednesday that Nicholas opened fire on Jones and Leonard after they "made contact" with him while responding to a dog complaint.
Officials have said little else about what happened before the shooting, which is being investigated by the Texas Rangers. Jeffrey Nicholas, 28, is jailed in nearby Tom Green County Detention Center on two charges of capital murder of a peace officer.
Hutchings, a city employee who helps with animal control, told the newspaper that the officers were helping city employees collect two dogs that had bitten someone earlier in the day.
The deputies had already caught one of the dogs and the other one ran into Nicholas' yard. Hutchings said Nicholas did not own either animal.