Are we allow to lay grass in HDB balcony?

I have not heard of any restriction on what u can do with it, unless it affects the building outlook. Even then, I have seen trees grow out of balconies /common coridors before in Marine Parade.

However, grass need full sun. That is why it is not possible to grow grass under shelter.

Also.. soil on floor = leaking downstairs. The methods to prevent a moist floor is expensive trays, with footings to allow air to evaporate the moisture on the floor. This is what HDB is doing on those carpark roofs converted to landscaping.