The main family law of Japan is Part IV of Civil Code (民法, Minpō). The Family Register Act (戸籍法, Kosekihō) contain provisions relating to the family register.
Here is an overview of the current civil laws and procedures for getting married in Japan. NOTE: Laws change. The following information is for guidance only.
In Japan, you can basically marry anybody you want, like your brother and sister, do that you little weirdo, unless you aren't and you are just curious on laws.