The federal government normally assigns ownership of data generated in activities that it funds to a grantee institution (i.e., UNH), not an individual (i.e., principal investigator).  As this study is federally-funded, the institution owns the data. 

Supposing this scenario takes place at UNH, the University assigns custody of research data that it owns to the principal investigator (faculty member) who is expected to discharge his/her custodial responsibilities in accordance with responsible data management practices as outlined in the UNH Policy on Ownership and Management of Research Data. As students and other study personnel at UNH may take a copy of UNH-owned research data related to their research, the postdoctoral student’s request to take a copy of the data with him is reasonable.