The Navy requires personnel to self-report if they have been arrested or are being prosecuted for a criminal offense - this is legal according to the Navy-Marine Corps Court of Criminal Appeals.
ALNAV 049/10 dtd 21 Jul 2010; and NAVADMIN 373/11, 08 December 2011.7, has amended OPNAVINST 3120.32C, which again requires reporting; if you have been arrested or if you are being prosecuted for a crime in state or federal court.
The law then
Prior to April 2009, the duty to self report existed and was found in the OPNAVINST cited above. Once the person self-reported the military could take various punitive or adverse administrative actions based on the underlying alleged criminal behavior. If a person did not self-report and the civilian case discovered, the person could be disciplined for a violation of Article 92, UCMJ, for an orders violation.
The law changed temporarily
In April 2009, the military appeals courts decided that the order to self-report was an illegal order and not enforceable. United States v. Serianne, 68 M.J.580 (N.M.Ct.Crim.App. 2009), aff'd, 69 M.J. 8 (C.A.A.F. 2010). the courts found the order unlawful, in violation of a members right against self-incrimination under the Fifth Amendment, U.S. Constitution.
The law now
As I have noted above, the SORM section 5.1.6., was changed. In United States v. Castillo, NMCCA 201300280 (N-M Ct. Crim. App. 27 May 2014), the Navy court has found the new regulation to be a valid order, and has affirmed a conviction for failing to report a DUI. The appellant in Castillo can now appeal to the Court of Appeals for the Armed Forces to challenge the order and the decision of the Navy court.
Like it or not, a Navy member who is arrested or is being prosecuted for a criminal offense must report this immediately.
However, there are several qualifications: (1) the person cannot be required to disclose the underlying facts, (2) any questions about the case must be preceded with a rights warning in accordance with Article 31, UCMJ, and there is a qualified immunity for use of the report.
What can happen
The member can still end up being prosecuted or disciplined by the Navy for the alleged underlying crime under certain circumstances. Also, adverse administrative actions might still follow, such as separation. Consult early on with an experienced military lawyer should you be in this unfortunate positoion