The answer(s) is yes & no... There is no death certificate as currently published and maintained in state records; however, the Army maintains records called Individual Deceased Personnel Files (IDPF) and they contain much of the same info. You can request these by writing to:
Commander US Total Army Personnel Command ATTN: TAPC-PED-F Alexandria, VA22331-0482
Provide as much of the following as you have: Full Name of Vet Service Number Unit Date of Death Your relationship to Vet
Be prepared to wait... it takes several months. Also, some of these records can be quite graphic... just so you know.