We present the results of a search for standard model Higgs boson production with decay to WW∗, identified through the leptonic final states e+e−νν,e±μ∓νν and μ+μ−νν. This search uses 360  pb−1 of data collected from pp collisions at s√=1.96  TeV by the upgraded Collider Detector at Fermilab (CDF II). We observe no signal excess and set 95% confidence level upper limits on the production cross section times branching ratio for the Higgs boson to WW∗ or any new scalar particle with similar decay products. These upper limits range from 5.5 to 3.2 pb for Higgs boson masses between 120 and 200  GeV/c2.