Election to managing committee on casual vacancy

Now you have explained the things correctly.

Now things are clear that :-

1. There is only one vacancy.
2. there are two candidates.
3. election authroity (returning Officer) is appointed.

How can there be two candidated (not three/frour) uless election is notified.  The rturning officer ( or election authroity) has to :-

1. Ask for voter list from MC.
2. Notify the election to all members and give time to all member to file nomination.
3. specify time fro scrutiny of papers.
4. specify time for withdrawal of nomination.
5. if nomination is only one then declare the candidate elected
6. if candidate is more than one the spcify time and place of election.

holding election by MC members only doe snot per-se sound legal.  You need to see the constitution of the Socienty and it is least likely to have such provision.  All members hae to be given voting rights.

As far a I could ascertain, casual vacancies in the Maaging Committees are to filled in accordance with Rule 56A-34 of the Maharashtra cooperative Socieities Rules, 1961 -

"56A-34. Casual vacancies how to be filled in:- In the event of vacancy occurred on account of death, resignation or otherwise, it shall be filled in by the society, according to the provision of bye-laws of the society,

Obviously, the bye-laws of your Society would provide you the answer/solution.

Byelaw No.128 of the latest Model Byelaws says as follows: 

A casual vacancy on the Committee may be filled by nomination out of a same class of Active members in respect of  which the casual vacancy has arisen as per provision of Sec 73 CB and as per the instructions issued by State Election Authority. 

The above means that the rules for General Election will apply to the bye-election also. The election officer deputed to the society has no alternative option. He has to follow all the procedures.