Do I need an inspection on a brand new home?
Yes. A new home can still have problems. Your own inspector finds them while the builder still has to fix them.
The city or county inspection only checks that the home meets the building code. Your inspector looks at much more, from the roof to the outlets.
If the home is still being built, an inspection before the walls go up can catch what will be hidden later. Another one before your warranty ends, near the 11-month mark, catches what showed up after you moved in.
Get every repair the builder agrees to in writing.
