Always cover the tops of the ceiling joists to make sure the insulation is deep enough to reach your target R-value and to prevent thermal bridging, the heat loss that occurs through the wood framing.

Is it safe to leave insulation uncovered?

Builders leaving fiberglass insulation exposed are in compliance with building codes because as long as the insulation is undisturbed. The American Lung Association agrees. This means if your attic or basement with exposed fiberglass insulation is used for storage only, there's no need to change anything.

Do you need to cover insulation?

Is Exposed Insulation Unhealthy? ... In this case, even if you don't plan on completely finishing the basement, you should cover the exposed fiberglass insulation for safety reasons, including: Disturbing fiberglass insulation can send particles into the air that act as lung, eye, and skin irritants.