A death certificate or Certificate of Death was an official report that documented the death of an individual. They could be invaluable sources of information when performing genealogical research. While researching her ancestor Shannon O'Donnel, Kathryn Janeway preferred such "raw material" sources to various histories of 21st century Earth, as she found them to all be biased. (VOY: "11:59")
Doctor Beverly Crusher hated making out death certificates, but was required to do so for Ro Laren and Geordi La Forge following their apparent "deaths" in 2368 as a result of a transporter accident. Ro observed her filling out the certificates, and thereby believed they were dead. (TNG: "The Next Phase")
Dekon Elig's death certificate was included in his file kept by the Bajorans in their Bajoran Archival Records. (DS9: "Babel")
Gul Darhe'el's death certificate was included in a file sent by Dukat to Odo in 2369. (DS9: "Duet")