"Luckily I found this: 'dear applicant, marry me for 25 years so one day we can scam a 3 day trip to Auckland. Yours etc.' Fingers crossed!"
Immigration New Zealand responded by contacting Laurie's Australian publicist and its own offices in Los Angeles and London.
However, there was no record of any interaction with Laurie or his wife, Jo Green, over a visa application.
New Zealand publicist Michelle Lafferty confirmed Laurie's tweets were intended to be humorous.
"Hugh was filling in the form and going through the usual red tape when it comes to visas. The tweet was intended to be tongue-in-cheek and certainly wasn't meant to offend anyone."
Ms Lafferty denied the tweets were a publicity stunt.
Immigration New Zealand area manager Michael Carley said the agency had no record of an interaction with Laurie over a visa application.
"Although Mr Laurie needs a work visa for his planned shows in New Zealand his wife as a British citizen does not need a visitor visa if she is planning to stay here less than six months.
"It is important to stress that NZ would not require any evidence from the couple about the genuineness of their relationship as part of Mr Laurie's work visa application."
Mr Carley said INZ had now received an email from Laurie's agent in Australia requesting information about the visa application process for him to come to New Zealand.
"The requested information about the cost and process was duly provided and an application from Mr Laurie will be processed in the usual way."
Laurie's band is due to perform at The Civic in Auckland on April 15 and the Michael Fowler Centre in Wellington on April 16.
He had earlier spoken of his excitement at coming to New Zealand.
"We're all thrilled to be coming to New Zealand to perform. I love the country, and the band loves air miles. We're going to put on a terrific show. I might wear a kilt," he said.
Read more: Hugh Laurie plots NZ tour
Luckily I found this: "dear applicant, marry me for 25 years so one day we can scam a 3 day trip to Auckland. Yours etc." Fingers crossed!
The impertinence of NZ's immigration authorities is eye-watering. Will I send them personal letters as evidence of the state of my marriage