It seems to me this could be misdemeanor or felony but I'm not sure.
So states have background checks which seems like the right answer.
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Virginia state law imposes restrictions on possession and transportation of firearms and ammunition, §18.2-308.2. That law restricts those who have been convicted of a felony, as well as those committing certain juvenile offenses. Separate laws, 18.2-308.1:1 et seq, address purchase, possession, or transportation of firearms by persons in various "mentally impaired" states. 18.2-308.1:3 specifically addresses involuntary commitment.
It shall be unlawful for any person (i) involuntarily admitted to a facility or ordered to mandatory outpatient treatment pursuant to § 19.2-169.2; (ii) involuntarily admitted to a facility or ordered to mandatory outpatient treatment as the result of a commitment hearing pursuant to Article 5 (§ 37.2-814 et seq.) of Chapter 8 of Title 37.2, notwithstanding the outcome of any appeal taken pursuant to § 37.2-821; (iii) involuntarily admitted to a facility or ordered to mandatory outpatient treatment as a minor 14 years of age or older as the result of a commitment hearing pursuant to Article 16 (§ 16.1-335 et seq.) of Chapter 11 of Title 16.1, notwithstanding the outcome of any appeal taken pursuant to § 16.1-345.6; (iv) who was the subject of a temporary detention order pursuant to § 37.2-809 and subsequently agreed to voluntary admission pursuant to § 37.2-805; (v) who, as a minor 14 years of age or older, was the subject of a temporary detention order pursuant to § 16.1-340.1 and subsequently agreed to voluntary admission pursuant to § 16.1-338; or (vi) who was found incompetent to stand trial and likely to remain so for the foreseeable future and whose case was disposed of in accordance with § 19.2-169.3...
Okay, that is who the restriction applies to. Now, the prohibition is
to purchase, possess, or transport a firearm. A violation of this subsection shall be punishable as a Class 1 misdemeanor.
"Firearm" means firearm, and "ammunition" is ammunition: they are subject to different laws. The felon possession law makes possession of ammunition illegal because the law refers to "firearm, ammunition for a firearm, or a stun weapon". The "involuntary commitment" law only restricts firearms, not ammunition. The background-check law 18.2-308.2:2 only regulates firearms purchases. See also this analysis of Virginia ammunition law, confirming that felon-in-possession is the one restriction on ammunition.
Federal prohibitions (18 USC 922) do include prohibitions on ammunition sales, see especially
(d) It shall be unlawful for any person to sell or otherwise dispose of any firearm or ammunition to any person knowing or having reasonable cause to believe that such person—...(4) has been adjudicated as a mental defective or has been committed to any mental institution;
(g) It shall be unlawful for any person—...(4) who has been adjudicated as a mental defective or who has been committed to a mental institution...to ship or transport in interstate or foreign commerce, or possess in or affecting commerce, any firearm or ammunition; or to receive any firearm or ammunition which has been shipped or transported in interstate or foreign commerce.
The penalty is in 18 USC 924:
(2) Whoever knowingly violates subsection (a)(6), (d), (g), (h), (i), (j), or (o) of section 922 shall be fined as provided in this title, imprisoned not more than 10 years, or both.