Police launched the investigation earlier this month after receiving complaints about three graffiti attacks targeting Dunedin street art and Ed Sheeran in the week leading up to the singer's Dunedin concerts.
The first incident happened on the night of Tuesday 27 March, when the Bath St Ed Sheeran mural was spray-painted with the words "Coyote **** u''.
The following Thursday night, two more pieces of street art were tagged on Princes and Manse Sts, again featuring vulgar attacks on Sheeran and references to Coyote.
A police spokeswoman said yesterday officers were"continuing to make inquiries into this vandalism,'' which included speaking to nearby business owners.
She would not confirm whether Dunedin police had made any arrests, issued any warnings or spoken to Coyote band members while the investigation was ongoing. Coyote comprises Dunedin brothers Jeremy and Louis Potts.
Asked whether they had been spoken to by police, an unidentified person messaging from the band's Facebook page said "nah, I don't think they really care to be honest''.
"Don't attribute it to anyone, sorry but we don't want to be part of any news stories,'' they added.
A Chorus communications box featuring a tribute to Dunedin band The Chills was also defaced earlier this year.
An expletive-laden video later surfaced appearing to show Coyote band members scribbling over the name The Chills and writing the name of their band underneath.
The graffiti has since been removed from all four sites.
Dunedin police (03) 471-4800, Crimestoppers 0800-555-111.
