Check if there is any proviso to the above rule.

If not than her posting is in violation of act, can challenge it in High Court, first complain to board. 

At least there must be some rule for appointment of supervisor, or role/authority/power of RMO in rules. If in rules, RMO has given supervisory power than on this point her appointment can be challenged and if no rule than board discretion will prevail.

Make it obvious only if RMOhold such post since decades.

Dear Queriest

You can file a writ petition with High Court praying Quashing of appointment as illegal and arbitrary.

Senior most among the same grade can be made incharge. 

Yes you can file a writ petition and counter the same

If a post does not occur in the organizational chart of a organization then it should be presumed that management wants to occur this post so if she is being paid for this extra burden or given some extra perks and facility then this can be challenged if she does not fulfill the criterion in a writ.

If you are confident that the post the lady medical officer holding is contrary to law and that you have been downgraded due to this then you can first make a representation to the competent authorities venting out your grievances and seek relief on this.

Let the authorities give you a reply by quoting the relevant rules and regulations in this aspect, after exhausting this remedy you may plan to approach CAT or high court with writ petition seeking remedy to this.

You have been advised to approach the authorities concerned with a written representation sent through proper channel venting out your grievances in this regard.

You first exhaust the remedies available within the organisation  after which you can plan legal action on this, if necessary or if there is any provision in law to satisfy your question in this regard.

1. As per the information mentioned in the present query, makes it clear the post making is the prerogative of the department depending upon the need of the time.
2. But at the same time, you are also correct in stating that for designating someone as In charge there must be some other conditions also need to be considered as in experience and expertise in the same work etc.
3. You should challenge it before the civil court of law, Hon’ble High Court seeking immediate intervention for giving clarification on the rules and procedures therein for appointing the same and putting stay on her appointment.

Dear

If there is no specific rule regarding appointment on the post of In-charge of your hospital then board can appoint any one on that post. 

If there is rule that Post of in-charge should be given to RMO then you can file a writ petition in high court challenging the appointment of lady medical officer.