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We examine the correlation between supernova (SN) host-galaxy properties and their residuals in the Hubble diagram. We use SNe discovered during the Sloan Digital Sky Survey-II Supernova Survey, and focus on objects at a redshift of z < 0.15, where the selection effects of the survey are known to yield a complete Type Ia supernova (SN Ia) sample. To minimize the bias in our analysis with respect to measured host-galaxy properties, spectra were obtained for nearly all hosts, spanning a range in magnitude of-23 < Mr < -17. In contrast to previous works that use photometric estimates of host mass as a proxy for global metallicity, we analyze host-galaxy spectra to obtain gas-phase metallicities and star formation rates (SFRs) from host galaxies with active star formation. From a final sample of ~40 emission-line galaxies, we find that light-curve-corrected SNe la are ~0.1 mag brighter in high-metallicity hosts than in low-metallicity hosts. We also find a significant (>3σ) correlation between the Hubble Residuals of SNe la and the specific SFR of the host galaxy. We comment on the importance of SN/host-galaxy correlations as a source of systematic bias in future deep SN surveys. [ABSTRACT FROM AUTHOR]