We have developed a COVID-19 vaccine, hAd5 S-Fusion + N-ETSD, that expresses SARS-CoV-2 spike (S) and nucleocapsid (N) proteins with modifications to increase immune responses delivered using a human adenovirus serotype 5 (hAd5) platform. Here, we demonstrate subcutaneous (SC) prime and SC boost vaccination of CD-1 mice with this dual-antigen vaccine elicits T-helper cell 1 (Th1) biased T-cell and humoral responses to both S and N that are greater than those seen with hAd5 S wild type delivering only unmodified S. We then compared SC to intranasal (IN) prime vaccination with SC or IN boosts and show that an IN prime with an IN boost is as effective at generating Th1 biased humoral responses as the other combinations tested, but an SC prime with an IN or SC boost elicits greater T cell responses. Finally, we used a combined SC plus IN (SC + IN) prime with or without a boost and found the SC + IN prime alone to be as effective in generating humoral and T-cell responses as the SC + IN prime with a boost. The finding that SC + IN prime-only delivery has the potential to provide broad immunity-including mucosal immunity-against SARS-CoV-2 supports further testing of this vaccine and delivery approach in animal models of viral challenge.