The Silver Star Medal authorized in 1932 was designed by Rudolf Freund of Bailey, Banks and Biddle. Silver Star Medal number #1 (with six oak leaf clusters) was issued to General Douglas MacArthur in August of 1932
The statutory authority for the Navy/Marine Corps to issue a Silver Star Award is 10 USC 6244. For the Army it is 10 USC 3746. For the Air force it is 10 USC 8746.
10 USC Section 6244. Silver star medal
The President may award a silver star medal of appropriate design, with ribbons and appurtenances, to a person who, while serving in any capacity with the Navy or Marine Corps, is cited for gallantry in action that does not warrant a medal of honor or Navy cross -
(1) while engaged in an action against an enemy of the United States;
(2) while engaged in military operations involving conflict with an opposing foreign force; or
(3) while serving with friendly foreign forces engaged in an armed conflict against an opposing armed force in which the United States is not a belligerent party.
SECNAVINST 1650.1G of 7 January 2002
NAVY AND MARINE CORPS AWARDS MANUAL
The first page provides points of contact, including the Navy Department Board of Decorations and Medals: (202) 685-1770
Paragraph 113. AUTHORITY TO APPROVE AWARDS
Subparagraphs (3) and (4)
[at page 12 of the PDF file, page 1-4 of the instruction]
"3. The Navy Cross, Distinguished Service Medal, and Silver Star Medal are approved and awarded by SECNAV in the name of the President."
4. The Legion of Merit, Distinguished flying Cross, Navy and Marine Corps Medal, Bronze Star Medal, Purple Heart, and Air Medal (Strike/Flight) are awarded by SECNAV and Chief of Naval Operations (CNO) or Commandant of the Marine Corps (CMC) under delegated authority from SECNAV in the name of the President.
SECNAVINST 1650.1G, page 2-43, [At page 82 of the PDF file] appendix C to Chapter 2, provides a sample SILVER STAR CITATION which appears to show that the signature of SECNAV is required.