There are any number of small avatar-rights movements going around, both in virtual worlds and even in some game-based MMOs. Does your avatar have rights? Is it a separate and distinct entity that can possess citizenship, rights, privileges and obligations in a different world (or virtual country)?
The short answer is, no. The rather longer answer is also no.
However much you identify with your avatar, and however much people react to it as if it were you, the fact remains that objectively your avatar is a representation, a vehicle and a tool. A useful tool definitely, and sometimes a wonderful tool, yes, but ultimately a device without intention.
Laws do not apply to tools (no, not even guns). Laws apply to people, and what people do (whether or not tools are involved). Sometimes there are special laws about what people may or may not do with particular and specific tools, but it is still about what a person does. An avatar isn't a person. An avatar is the expression and representation of a person.
Your avatar isn't a citizen of a place under different laws. It can't be in fact, because it is just a tool. When the law reaches out, it reaches out to you, the person in the chair. An avatar has no will or intention in much the same fashion as a screwdriver, a cigarette, a ladder or a firearm has none. But you do, and the law will hold you accountable for your actions when or if you choose to break it, regardless of the tools you choose to do it with.
Likewise, a tool has no rights, no responsibilities and no obligations. A tool cannot have citizenship as it is basically not capable of choice. Only you have the ability to make choices, so only you can have these things. (It is to be noted, that the law has certain exceptions and allowances for situations where a human being has no will, choice or intention).
Should it come to pass that your virtual world operator or MMO operator decides to enact a Bill of Rights, those rights of course, will apply to you, the person. Not to your avatar. The person; not the tool, not the costume, not the vehicle. Those rights, if granted to you, would not be permitted to conflict with those of your own country without your own government's agreement.
When this topic comes up, one of the things people immediately think of is one avatar shooting or killing another, and that the law cannot devolve upon the user because it would be nonsensical to charge a user for battery or murder on that basis.
And they'd be right. Because no battery or murder of another person actually takes place in such a case. Avatar violence is a Punch and Judy show (and often about as annoying). If you figured out how to cause real physical, financial or emotional harm to another person, then the law would apply as it always has - regardless of the tools involved (except for some very over-specific, narrowly-drafted laws, which are thankfully in the minority).
In the end, many discussions about rights, obligations and civil governance in virtual worlds are hampered by the misunderstanding of the basic nature of an avatar and of it's relationship to the user. An avatar is a tool we can project our identity into, but the actions, decisions, choices and legal rights and obligations remain our own.