You aren't declaring a variable with that line you are creating a game object and assigning it to a variable. It appears this code is looking for a player game object that is local and creating one if there isn't one.

Well I solved it by changing:

GameObject localPlayer = new GameObject();

to:

GameObject localPlayer = null;

Thanks for the help, both of you. I didn't realize new GameObject() would actually place an empty GameObject in the scene.

public static GameObject FindLocalPlayer() {
    GameObject localPlayer;
    GameObject[] Players = GameObject.FindGameObjectsWithTag("Player"); 
    foreach(GameObject Player in Players) {
        if(Player.networkView.isMine) {
            localPlayer = Player; 
        }
    }

    if(localPlayer) {
        return localPlayer;
    } else {
        return null;
    }
}

Or perhaps using System.Linq;

public static GameObject FindLocalPlayer() {
    var Players = GameObject.FindGameObjectsWithTag("Player"); 
    return Players.SingleOrDefault(o=> o.networkView.isMine);
}