The legality of trapping a Madison rat depends on the country you reside in. Due to the fact that Wisconsin rats can easily cause a lot of damages, there is no country in the world that completely prohibits the trapping of a rat. However, some restrictions exist. Some rat trapping techniques include:
Leghold traps mostly catch a Madison rat by the leg. The implication is that the rat is trapped, but doesn' t die, thus making the Wisconsin rat to suffer. Countries that are particular about animal rights have made this illegal. Thus, if your country values animal rights, then they don't want you to use this type of trap.
Most countries allow the use of dogs for trapping Wisconsin rats. There is, however, the risk of the dogs getting infected by rabies that could be carried to the rat. The rat could subsequently spread such rabies to humans.
Poison is another means of killing rats that a lot of people prefer. While this is a great option as well, some countries are careful about making it legal due to the risks. If there are children or the poison gets mixed with food, it could lead to harm or death of people in the house. There are also countries where there have been reports of people committing suicide with easily accessible rat poisons.
Extermination is allowed in virtually all countries in the world. It is, however, sometimes restricted to the use of only Madison professionals to avoid risks.
In most cases, countries that have restrictions only do so to avoid trapping the rats for long without killing it, where at the end of the day they will be badly hurt. If they are cages, that trap without killing so that you can send them back to the wild, then all countries allow that. If they are traps that capture and kill almost instantly, almost all countries allow that. If they are traps that capture, without killing while harming the animal or leaving them in pain, no country allows that.