A post-mortem examination found the father of three adult sons was killed by a severe blunt-force blow to the head.
Mr Griffin had been working on alterations to a garage at the rear of his house, where he lived alone, when friends found him seriously injured.
It is not known when the assault happened, but police believe it was early on Sunday.
A team of police and specialists continued to examine the Second Ave property and expected to complete that today.
Mr Burke urged residents in the avenues area to check their backyards for "foreign objects" as officers searched for a weapon believed to have been used. He said the weapon could include, but was not limited to, a hammer, a lump of steel or a piece of wood.
Mr Burke also urged people to come forward if they had discovered a piece of clothing on their property during the last few days.
Mr Griffin's family and the investigation team appreciated the help from the Whangarei community.
They still urged anyone who had information to contact officers on 09 430 4500 or Crimestoppers anonymously on 0800 555 111.