Yes, you need carbs to build muscles efficiently, but if you don't mind slower progress, you can build muscle even on low levels of carbs.

How much depends to a large extent on your muscle mass. It's very individual. Even adding 25-40g of dextrose around my workouts allows me to build muscle at a reasonably fast pace.

Even on induction levels of carbs, though, I added 6lbs. of LBM while losing 4lbs. overall, over the course of 9 or 10 months doing barely any exercise. The high-protein supports muscle development and maintenance on its own--and don't forget that your body can convert protein to carbs if it has to.