Our actual costs for our granny flat were much higher than they should have been (contractor issues). We explained that to the assessors office and they looked over the original contract.
Additionally, they reduced some of the cost for things that were ADA compliant. (We were building a handicap accessible granny flat for my wheelchair bound father in law.) There’s a law that says they can’t increase your assessment if your addition or improvement is to make the property accessible. So we got a reduction to account for the extra grading for the ramps, and for extra costs to make the bathroom fully accessible.
I would NOT lie or make up a number on the form – but I would work with the assessors office to make sure it’s accounted for properly.