What is the reason for topdressing with compost? Are you trying to get your OM levels up? Because there is a much less expensive way to do that.
In my neighborhood, compost delivered to the door costs about $70 per cubic yard. If one cubic yard covers 1,000 square feet, then the cost is $70 per 1,000 square feet. But if I can buy alfalfa pellets at the feed store for $12 in a 50-pound bag, and it goes on at 20 pounds per 1,000 square feet, then the cost of organic fertilizer is $4.80 per 1,000 square feet. I can apply an excellent organic fertilizer 15 times for the price of compost. Fill in your own numbers. If you can get a yard of compost in the back of your truck for $35, then the cost of compost is only $35/1000. Still I can fertilize 7 times with real fertilizer.
The total N content in compost is about the same as in one app of fertilizer. Compost is not cost effective as a fertilizer.
Now how you improve the OM in your soil? By growing roots. Besides microbes, roots are the most massive OM in your soil. More roots, more OM. Applying fertilizer 10 or 15 times is much better at building roots than applying compost. Grass is one of few plants that sheds its roots. Every year it loses about 1/3 of the roots and regrows new ones. Those roots it loses become OM in your soil. So the more roots you grow the better your OM becomes.
Then what is compost good for? Compost is great for restoring the microbial species and population to your soil. If your soil has become depleted from drought, flood, or chemical spill (including herbicide, insecticide, fungicide, and chemical fertilizers), then compost is the fastest way to restore the biology to the soil. Not compost tea, compost. Compost is also excellent as a micromulch. You cannot mulch a lawn with something like bark mulch, but you can apply compost to get some of the same effect. Mulch is excellent for holding moisture content steady for long periods of time. One of the best ways to improve unimproved soil is to mulch it for several months. But if you already have a lawn, then your soil is improved and getting better.
Now after I've launched into several rants, you're going to tell me you are topdressing with compost because someone gave it to you and you don't know what to do with it.