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- nu nu,+/-mu -/+nu nu and mu+ mu- nu nu. This search uses 360 pb -1 of data collected from pp collisions at square root of 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.