The British second seed, 29, beat world number 82 Rosol 4 6-3 6-2 in a warmed match at the Munich Open a year ago.
English number two Dan Evans confronts American Rajeev Ram, while Kyle Edmund will play France's Richard Gasquet.
Briton Johanna Konta, seeded a profession high thirteenth in the ladies' singles, meets American Bethanie Mattek-Sands, who won blended twofold gold at the Rio Olympics.
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