Douglas County Sheriff's Office tweeted deputies responded to a domestic disturbance Sunday morning that resulted in shots being fired.
Parrish was with the sheriff's office for seven months. He's survived by a wife and two young children.
People in the area are being advised to shelter in place and others are being asked to avoid the area.
People watch a procession of police vehicles escort the hearse carrying the body of a deputy killed in a domestic disturbance where multiple deputies and civilians were shot in Highlands Ranch, Colorado, on December 31, 2017.
County officials set up an emergency shelter for those displaced by the incident, citing the "size and scope of the investigation".
CNN said the incident happened at the Copper Canyon Apartments in Highlands Ranch, about 20 miles south of Denver. Another nearby hospital said it received four patients but wouldn't release their conditions. It's not known if they are law enforcement.
East hospitals restrict patient visits because of increased flu numbers
County health officials said six more deaths were reported this week, as were 3,873 confirmed cases of the illness. However, county officials stressed that "In reality, every year is a bad flu year for the people who get sick".
There is a fund for fallen officers in Douglas County.
Our thoughts and prayers are with the Douglas County Sheriff's Office and the family and friends of Deputy Parrish.
Deputy Jason Blanchard was quaoted by the paper as saying: "We have multiple officers down".
The call to protect and serve too often leads to this ultimate sacrifice.
This is an active situation in Colorado that we will be following throughout the day.
The identities of the two injured civilians were not immediately disclosed, but Spurlock said he believed they are residents from other apartments.