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This answer is to your query:
There are two provisions in our Indian Law that relates to the election of a person, who is not a member of any house of legislature but becomes a Minister due to some uncertainties, within six months. This is to retain his position therein post six months.
1) According to Article 164(4) of the Indian Constitution, a person who is not a member of the state legislature can still be appointed as Chief Minister or any Minister for six months. However, within that time, he should be elected to the state legislature, and if he fails, he ceases to be the concerned Minister.
2) Section 151A of the Representation of the People Act, 1951 reads as: "A bye-election for filling any vacancy referred to in Sections 147, 149, 150, and 151 shall be held within a period of six months from the date of the occurrence of the vacancy:
Provided that nothing contained in this section shall apply if—
(a) the remainder of the term of a member in relation to a vacancy is less than one year; or
(b) the Election Commission in consultation with the Central Government certifies that it is difficult to hold the bye-election within the said period.
The above two provisions, undoubtedly, mandates the Election Commission to conduct by-elections within six months to fill the vacancies.
Similarly, there is another stipulation, that is, in a State where there is a bicameral Legislature (Legislative Assembly and Legislative Council), the Minister can retain his position by getting elected to either of the houses. In Legislative Council, there is an indirect election, so it is comparatively easier to get elected to Legislative Council than to Assembly. For Instance, Maharashtra Chief Minister Uddhav Thackeray was elected to Legislative Council to retain his position as Chief Minister.
This was possible because Maharashtra has a bicameral Legislature. However, only few states have this facility. While many states in India only have a Legislative Assembly, and in such States, it is important to get elected to the Assembly. Same is the case in Uttarakhand because it doesn't have a bicameral Legislature. Ex-CM Tirath Singh Rawat, who got appointed as CM in March 2021, needs to get elected as MLA within September 2021, otherwise he ceases to be a Chief Minister.
It was submitted on their part that there could be no chance of elections due to the pandemic situation. Therefore, Rawat resigned from his position
However, if you read Section 151A more carefully, you can find two proviso which makes it clear that it was not a self-made decision but an inevitable situation. The proviso states that in two circumstances, it is not necessary for the ECI to conduct by-elections. One, if the remainder of the term of the member in relation to the vacancy is less than a year, and two, if the ECI certifies that it is impossible to conduct elections owing to some circumstances.
With respect to Uttarakhand's political crisis, both the proviso applies. The tenure of the government began in 2017 and has less than a year to end. Similarly, due to the current pandemic scenario, it also seems impossible to conduct elections. Therefore, in either of the cases, by-elections need not be conducted. With no by-elections, there is no chance of Rawat to get elected as MLA. And with no such election, there is no possibility to retain as CM. Therefore, altogether, it is certainly impossible for Rawat for not getting replaced. Keeping in mind all these complications, the Ex-CM may have resigned before hand.
However, this doesn't mean that he cannot be elected again and become CM. There is still a possibility as it happened with Punjab Congress leader Tej Parkash Singh in 1995.
Hope this helps!