Edit: In response to the new rules, I'm rewriting the OP to be more expansive. Again, keep in mind that I take this as silliness and OOC/IC, and none of the answers are considered to represent their nations' true policies.
What sort of laws governing private ownership of nuclear, thermonuclear, radiological, biological, and chemical weapons exist in your nation? Are there officially such laws, or are they implied? If so, then how are they worded, have they ever needed enforcing, or if not, has this strange freedom ever been used?
Yukonastan is known for fairly liberal weapons laws. Most people do own weapons that under other regimes are completely outlawed, restricted, or otherwise disliked. These include rifles, shotguns, hand guns, automatic weapons, autocannons, and large-bore howitzers. These are officially regulated. However, some weapon owners go above and beyond the aforementioned list of weapons, and do own thermonuclear warheads.
The international regulations, and Yukonastan's regulations, regarding weapons of this nature have never specified anything about civilian ownership, and as such, it is considered legal under our justice system. Yukonastan's justice system has a stance of "Legal unless Otherwise Specified", which is the reason why. However, it must be noted, that due to the pile of licences and licence requirements, you will need a letter of approval for each warhead you plan to own.
Despite these regulations, nuclear weapons are still rarities, due to licencing issues. Nuclear weapons specifically qualify variously as radiological, nuclear, biological, or other hazardous products and/or wastes (environmental law), explosives (explosives law), any other weapons (weapons law), devices designed to be capable of causing death, injury, and/or other serious bodily harm (military industrial regulation), and devices capable of producing fire, wind, shockwaves, and/or similar disruptive events (noise ordinance). In short, to own a nuclear warhead capable of firing, you need the following licences, as well as a letter of approval:
Environmental cleanup licence - Class NRB (Nuclear, Radiological, Biological)
Weapons owning licence - Class F3 (Any Other Weapon, subset Explosive)
Explosives owning and operating licence - Class J (Explosives rating in kiloton to megaton range)
Military industrial safety training course certificate - Type S (Explosive, radiological, nuclear, otherwise hazardous)
Noise licence - Class U (Unrestricted)
As a prerequisite for said licences, you need to be:
A registered individual with an environmental cleanup organization (ECL-NRB)
Mentally checked, criminally cleared (WL-F3)
In possession of approved storage location (EOL-J)
Mentally checked, criminally cleared, in possession of (ECL-Any) or equivalent. Completed an approved training course satisfactorily (MSTCC-S)
Mentally checked, criminally cleared (NL-U)
When you have all of those licences, and qualify for all their prerequisites, you may apply for a letter of approval, and it entitles you to own one nuclear warhead of the type on the letter. Nothing of course prevents one from applying for, and receiving, multiple letters of approval.
In practice, this makes owning a nuclear warhead a rare, but not unknown, occurrence. Within this small subset of the population, the preference for nuclear devices lies at the low end of the scale, from Davy-Crockett-like devices at ten to twenty tons of yield, to W33-like tactical warheads, with a yield closer to the kiloton range. There is a single designated range which is certified via executive decision for detonation of such weapons up to 20kt, above ground, if you book the range in advance.
Once a warhead has been detonated, its letter of approval is to be destroyed by a government agency, as is the document containing the warhead's serial and tracking information. If this isn't done, you may be charged for holding an unapproved letter of approval.
That's a short recap of how legal it is to own a nuclear weapon in Yukonastan, with biological, radiological, and chemical weapons being under similar regulations.
How do the laws regarding the ownership of nuclear weapons within your nation stack up with this?
Remember: "If pocket nukes are outlawed, then only outlaws will have pocket nukes."