The format for a press release reference is very similar to a reference for an online newspaper article and the Chicago Referencing Guide covers this under Journals, Newpapers & Magazines - see direct link below.
Australian Government press release example
Footnote:
Australian Government Department of Defence, "First new Guardian Class Patrol Boat Launched," May 30, 2018, https://www.minister.defence.gov.au/minister/christopher-pyne/media-releases/first-new-guardian-class-patrol-boat-launched.
Bibliography:
Australian Government Department of Defence. "First new Guardian Class Patrol Boat Launched." May 30, 2018. https://www.minister.defence.gov.au/minister/christopher-pyne/media-releases/first-new-guardian-class-patrol-boat-launched.
The Chicago Manual of Style Online (section 14.200) provides a further example - see link below.