The robber was handed "an amount of cash", before walking out of the bank on foot and heading east along Jackson St, Petone's busy main road.
"We are very concerned, as inquiries revealed the male went into Kiwibank initially to write the note that he later took to BNZ," said Detective Sergeant Ben Quinn, of the Wellington crime squad.
"He went into the bank, wrote the note on their slip and then left to present it at the BNZ.
"There was no attempt to use the note at Kiwibank nor to interact with staff there, however, as you can imagine we are very keen to find this man."
The robber is described as Maori or of Pacific Island descent, with a stocky build.
He was wearing a light-coloured top, dark pants and black beanie, with a bag slung over his shoulder.
Police are appealing for sightings.
Anyone with information can call Lower Hutt police on 04 560 2600 or Crimestoppers anonymously 0800 555 111.