Kelly was responding to an answer by Sturgeon to a parliamentary question about the quango's decision to proceed with the project, apparently without securing standard indemnity agreements with owners of major pipelines along the intended route.
The subsequent need for difficult post-facto negotiations with the companies resulted in a long stand-off that caused the suspension of the project for more than a year, raising the risk it would be abandoned.
In her previous answer, Sturgeon said the insurance issues "have now been resolved and completion of the project is expected by July 2014". However, she failed to provide any explanation for the apparent failure in project management.
Kelly said: "This situation appears to have been entirely avoidable. It strikes me as very strange that a major infrastructure project would begin work without the basic agreements in place."
In his letter dated December 20, Kelly writes: "You note in your reply that the issues have been resolved and that the project is scheduled to finish in 2014. My concern is that the issues occurred in the first place given the stall was the result of what appears to be a lack of basic due diligence ... It seems highly unusual, and somewhat reckless."
According to the Scottish Government, Scottish Water's construction of a new outfall pipeline from the sewage works at Kirriemuir is required "to secure environmental improvements to the River Dean water and in particular to protect and enhance aquatic life".
The Water Industry Commission for Scotland, established to act as a watchdog of public investment, has previously declined to comment on the case, saying "what we are not able to do is take an individual project and say they should not do this or not do that".