On probation but stopped going to company on medical grounds - notice mandatory?

Hi, I have recently joined a Ltd company on probation for about 1 year but within a few days of joining i had stopped going to company and communicated to them reason for medical grounds after few days but just on the 1st day of the month i received part salary for the no. of days from when i joined the company from payroll department. It is just a few days and my question is i have not yet tendered any resignation letter to them and the stipulation mentioned in the offered letter clearly states that :- i) It is mandatory to serve one month notice period in case of resignation of service after confirmation. But during probation also it is given that i have to serve one month notice and one month salary in lieu of notice period is not acceptable.
There is no point of legal actions that could be taken mentioned but if i again join donot want to join the company what should be my course of action from here on. Should i give any medical certificate but that would give the impression that i am fit to join for service again.
Thanks and Regards,

Resignation Letter is a must to terminate the employment, instead of just walking off you would have tendered your resignation. Now since your employment has not send you any letter, stay calm and wait for their reaction if any.

Dear Paku, why have you stopped from going for work? are you sick for ever? Please come out with factual position about your sickness.Will all sick people think of quitting job? waht is the nature of sickness?

Dear Paku,
It is not quitely understood why you have stopped going to work, sickness is a plea. If really you do not want to continue the job better send your resignation. It is otherwise you will be in problem for future job.
Regards

It is always better and recognized procedure to give letter of intimation (though you are in probation period) to your employer that you are leaving the service. By this letter your employer will know that you will not come for duty and he will make alternate arrangements for his work.