No. No US state has designated an official "state grass."
States enthusiastically adopt official symbols—birds, flowers, trees, fossils, soils, dinosaurs, even state microbes (Oregon: Saccharomyces cerevisiae)—but grasses have been overlooked. Some states recognize state wildflowers or state flowers that happen to be grass-like (e.g., Texas bluebonnet is a legume, not a grass), but no legislative act has crowned a grass species.
If you're designing a state-symbols trivia night, "state grass" is a trick question. The answer: none.