"And if these [nails] were to become dislodged they are like missiles, someone could also walk on it. Things like that really annoy me, especially if someone is doing it deliberately because it's such a cowardly thing to do and for what reason? it's just stupid," Miss Te Tau said.
She said Z nails were hard to see and drivers were unlikely to know they had run one over until their tyre went flat.
The areas where people have reported possibly running over them are the Kuripuni shopping area, around Pak'n'Save, and by the Colombo Rd bridge.
Miss Te Tau said she thought someone was probably dropping the nails deliberately but that it could also be someone losing them from the tray of a vehicle, not realising they were falling off.
"It's a bit of a mystery, it really would be good to get to the bottom of it."
Senior sergeant Jymahl Glassey said police had received numerous complaints over the last two weeks about Z nails causing punctures and that it appeared someone was "purposely depositing Z nails in the path of vehicle traffic".
Mr Glassey said there was real risk someone could be injured, or killed, if a crash happened as a result of a puncture. "It is important that police are able to establish the cause of these occurrences and ensure safety on our roads."
Police would like to hear from anyone with information and ask they call the Masterton Police Station on 06) 370 0300 or Crimestoppers, anonymously, on 0800 555 111.