Instead of quoting laws to the company prefer to quote the reasons in the notice of resignation and attach the medical record and advice of the doctor showing need to get proper treatment and bed rest required for it.
The notice of resignation and subsequent communications are the documents on record and should be carefully structured to suit the long term interest of the employee.
The organizations usually perceive the medical reasons quoted are to get away from serving full notice period as per appointment letter or any service agreement/bond signed by employee.
Resignation can be without permission and notice.
If there is a provision for notice pay in lieu of notice period then employee can affirm to tender notice pay in lieu of notice period.
The employer has the power and discretion to waive off the notice period and notice pay and on your request it may waive off too.
Such matters are best resolved by applying rapport, goodwill, and exceptional levels of persuasion, persistence, negotiation, reasoning skills. These skills can be acquired and employee should endeavor for it.
Other view point is that companies are known to state in appointment letter that employment can be terminated due to prolonged absence from duty due to sickness.
If it is so then employee should also be allowed to terminate the contract of employment in situations that require prolonged medical treatment.
You may download standing orders applicable to the establishment and extended to your designation, leave policy, exit policy, severance policy, HR policy, service rules etc and if required obtain legal opinion from your labor consultant/service lawyer.
If you have to submit a leave application then submit it along with medical certificate of the doctor and keep proper record of all prescripttions, medical bills, diagnostic reports etc...............
There are many threads on such matters that you may find relevant e.g;
https://www.lawyersclubindia.com/forum/Is-serving-full-notice-period-necessar-instead-waive-off-opt-92538.asp#.UpQZ8NIW1MA
https://www.lawyersclubindia.com/forum/Notice-period-nad-absconding-employee-92345.asp#.UpMpStIW1MA
https://www.lawyersclubindia.com/forum/Mnc-issuance-of-experience-certificate-re-leaving-letter-92229.asp#.UoiogdKAqWM
https://www.lawyersclubindia.com/forum/One-sided-notice-period-92171.asp#.UoiondKAqWM
https://www.lawyersclubindia.com/forum/Query-regarding-relieving-letter-and-continuity-bonus-92151.asp#.Uoio6NKAqWM
https://www.lawyersclubindia.com/forum/Whether-notice-period-has-to-be-given-during-probation-91808.asp#.UoSg3nCAqWM
https://www.lawyersclubindia.com/forum/Notice-period-92146.asp#.UoTD33CAqWM
https://www.lawyersclubindia.com/experts/Different-notice-period-for-employee-and-employer-during-probation-432151.asp#.UoTGvHCAqWM