Static cling is one of those annoying things that happens to sheer blouses and other clothing items as the air becomes dry. This electrical buildup develops from friction between two dissimilar fabrics and is relatively straightforward to resolve, once you determine the solution that works best for you. You'll probably even find yourself putting that sheer blouse back into frequent rotation.
Items you will need
Spray the blouse with a commercially-available anti-static spray. This is most easily done while the shirt is still on the hanger.
Spray a light coat of hairspray on the blouse in lieu of a dedicated anti-static spray. This works best if you lightly spray yourself prior to donning the blouse.
Use a moisturizer. Static present in clothing is reduced if your skin isn't dry as well.
Toss your blouse on low with a dryer sheet in your clothes dryer. Once you remove it, the static should be gone.