The structure, magnetic response, and dielectric response of the grown epitaxial thin films of the orthorhombic phase of YMnO3 oxide on Nb:SrTiO3 (001) substrates have been measured. We have found that a substrate-induced strain produces an in-plane compression of the YMnO3 unit cell. The magnetization versus temperature curves display a significant zero-field cooling (ZFC)-field cooling hysteresis below the Néel temperature (TN ≈ 45 K). The dielectric constant increases gradually (up to 26%) below the TN and mimics the ZFC magnetization curve. We argue that these effects could be a manifestation of magnetoelectric coupling in YMnO3 thin films and that the magnetic structure of YMnO3 can be controlled by substrate selection and/or growth conditions.