"We remain concerned that no formal funding agreement for this massive project between Auckland Council and the Government is in place, yet the physical construction has begun. We believe that a number of red flags remain for Auckland ratepayers."
The Office of the Auditor-General confirmed receipt of the letter and said it will now "fully consider the concerns raised".
Auckland Transport estimated CRL build costs of $2.5 billion and completion for 2023, with Mayor Len Brown saying he wants the council to negotiate a 50-50 payment split with the Government.
An AT spokeswoman denied the project's budget had increased but admitted "it is almost certain to change because the design detail has yet to be completed".
Asked about Mr Key's prediction of rising costs, the spokeswoman said he had "a very good understanding of the project and how major infrastructure works".
"Ratepayers and taxpayers should always be concerned that they are getting value for money.
"They can also have confidence in the robust level of scrutiny, planning and design that has gone into the CRL and the strong national and international team that has been hand-picked to get it to happen."
Transport Minister Simon Bridges said he was waiting to see more accurate costings.