I expect you can find a specialist where you purchase the turf. These are the people who grow the grass and cut it from the soil when you are ready for delivery. We call them sod farms here. I guess you call them turf farms. If they don't lay it themselves, they will be able to recommend someone who does that.
Now, I don't think you want it perfectly flat. You have to have a grade and it should slope away from your house. The slope should be a certain degree for your area depending on the your landscape. So, please don't say "flat" or someone might follow your instructions. LOL
You say "very fine" and that refers to the texture of the leaf blade. Is that what you mean? If so, it wouldn't depend on your specialist laying the turf but on what turf you select. When you locate a sod/furf farm, you will probably be able to choose the grass you want.
Please let me know if I answered correctly to make sure I understood your question.