Grading backyard question

I have a 2000 plus sq ft backyard that need grading to bring it to an even slope. Probably 5 to 10 cu yds of dirt spread by a bobcat will do the job. The low spots to be filled in will be no more than one or two inches of dirt. Most of the lawn will not need any dirt fill.
The dirt gone pretty hard over the years (24) and the grass OK. The weeds there are mostly dandelions with some stinkweed and assorted broadleaves. They are not that many I can easily remove them by applying killex and some hoeing as I had been doing every year. They do keep coming back because my lot is next to a school field cum public park.
When I built the house, yup I was coordinating the tradesmen and did some sweat equity myself, I didn't have enough money to grade this part properly and its uneven in some places and lumpy in other spots. I had held off building the rear deck because all this time I did not want to have the deck in place before the bobcat can do its work. Talk about procrastination.
The question is can I just spread the dirt over the grass and grade the slope or do I need to dig up all the old grass first. As far as I am concerned the present grass species is perfectly OK since whatever species of grass I put in the present one which is the same as that of the school field will take over anyway.
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If it was me, I would roto-till the area before adding more dirt, but it's probably not necessary. What's buried under there, and how deep?
PaPaPeng wrote:

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wrote:

It was a former wheatfield. When they rezoned it for residential development most of the topsoi lwas removed leaving perhaps only 2 to 3 inches put back to nutrure the grass. The dirt below is real sticky clay. On open building lots easily 1/2 to 3/4 inches of wet clay can build up on the shoe soles by just walking on the stuff. Fortunately my front and back yards slope outward so there is no stagnant water around the house.
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I'd get the total topsoil depth to 6 to 9 inchs if I could, depending on the grading. Considering the effort involved in doing this, it's worth doing it right, so the grass will have a good root system. In areas where only a couple inchs of topsoil can be applied, I'd rototill some humus material in. Anyplace where the grass won't be killed by covering it, I'd kill it with Roundup. You're going to have to reseed anyway, so you might as well do the whole thing with a good grass. I'd look at getting the best seed you can find for the application. I'd check online sources like seedland.com, as they have better varieties and more choices than the local home centers. The newer seeds can have better resistance to disease, better color, better drought tolerance, texture, etc.
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