In order to get the statues, the player must tell Nook two certain passwords; one for the Mario statue, the other for the Luigi statue. One set of codes was released by Nintendo Power, which can be proved by telling Nook a certain password for either statue, and when entered, he'll say "Oh, yes. This prize just came in from Nintendo Power." There is another code to get them, but it appears to be won from a glitch, backed up by the fact when the special password is finished, he will say the player won it from a contest, but the contest's name is glitched letters.
At random, villagers may bury the Mario statue and post about it on the Bulletin Board. They will specify which row of acres the statue is hidden in, and it will appear on the map as a brown mark on the ground (the same one that specifies a buried fossil or buried Bells). If the player claims the buried statue in time, it will be theirs.
The Luigi Trophy is also available from Crazy Redd in the GameCube version of Animal Crossing for 28,000 bells.
The Mario statue is golden, referencing the fact that Mario is highly recognized as Nintendo's main icon. He is standing tall and proud. The Luigi statue is Silver, referencing that Luigi is often seen behind Mario. Luigi is taller than Mario and is slouching, perhaps meaning that he's a little depressed that Mario is often the spotlight while he is not. The Mario statue is also a possible reference to Kirby Super Star, where one of Kirby's transformations with his Stone Ability is a golden Mario statue flashing his trademark "V-Sign" in the air. Unfortunately, in those Kirby games, there is no Luigi statue.