Chief Minister can hold office without being an elected representative of people!
Unelected representative in democracy:
A grievance was raised that respondent Nos. 1 and 2 were not qualified to be appointed as Chief Minister and Minister respectively as they were members of the Rajya Sabha (Upper House of Parliament) and thus disqualified under Article 164(4) read with Article 164(1) of the Constitution. The basic stand is that since they were members of the Rajya Sabha the requirement of their being elected to the State Legislative Assembly within a period of 6 months does not apply to them as they are already legislators of the Rajya Sabha.
There is no bar in Constitution prohibiting appointment of a person as Minister or Chief Minister, without being a member of the State Assembly.
The absence of the expression from amongst members of the Legislature in Article 164(1) is indicative of the position that whereas under that provision a non-legislator can be appointed as a Chief Minister or a Minister but that appointment would be governed by Article 164(4), which places a restriction on such a non-member to continue as a Minister or the Chief Minister, as the case may be, unless he can get himself elected to the Legislature within the period of six consecutive months from the date of his appointment. Article 164(4) is therefore not a source of power or an enabling provision for appointment of a non-legislator as a Minister even for a short duration. It is actually in the nature of a disqualification or restriction for a non-member, who has been appointed as a Chief Minister or a Minister, as the case may be, to continue in office without getting himself elected within a period of six consecutive months.
Mystery of Law and Justice 