I think requirements of internal democracy are quite general.
Spanish constitution as another example:
Article 6. Los partidos políticos (...) Su estructura interna y funcionamiento deberán ser democráticos.
My translation:
Their [of political parties] internal structure and function must be democratic.
The law on political parties is more specific (article 3 j), when stating what should be in party bylaws:
j) El procedimiento para la elección de los órganos directivos, bien directamente o por representación, que en todo caso deberá garantizar la participación de todos los afiliados mediante sufragio libre y secreto, y los procedimientos de control democrático de los dirigentes electos.
My translation:
The process to elect directive positions, directly or by representations, that in any case must allow participation of all members through free and secret suffrage, and the democratic control of elect directive members.
Articles 6, 7 and 8 expand on that.
Update:
The sources pointed by CptEric ask for a minimum of 3 members as any other association. However, I'm not sure about if a party could be registered with less members, mainly because the law of political parties doesn't reference the laws about associations, which aren't uniform in the whole country. Probably, if a party were rejected registering because of lack of enough members, the issue could end in court.