Cedric John Maniapoto, 58, was found dead at an address on Ohautira Road on Tuesday at 8.15am.
On Friday police said that same morning, just over an hour earlier, a dog called Napier showed up in a store in Te Uku, a farming settlement east of Raglan. It had a gunshot wound.
"This store is roughly seven kilometres from the scene, and it has not been established how Napier got to the store with his injuries," Acting Detective Inspector Andrew Saunders said.
"Napier, a medium-sized brown and white dog, is a lucky survivor of his injuries and is recovering well."
He said anyone with information or that noticed anything unusual in the area should get in touch with police, referencing file number 240305/1701, or Crime Stoppers on 0800 555 111.
"The area is busy during the day but is quiet at night, and we are interested in speaking to anyone that saw another person or vehicle while passing through the area.
"We would like to hear from anyone that may have seen a dog on the road between the scene location and Te Uku, or if anyone delivered Napier to that location."
Police were also interested in any dashcam footage from Ohautira Road from late Monday evening to Tuesday morning.
"It is devastating for Mr Maniapoto's whanau to have to prepare to farewell after a loved one who was so unceremoniously taken away, and we are determined to find who is responsible," Saunders said.
RNZ