Equal Notice Period From Employer And Employee

hi am working in Public Sector Bank and facing a trouble..I put in my paper and given one month's notice but my offer letter only says that "during probation period bank can terminate ur services by giving One Month's notice".
it never mentions if i can also resign by giving one months' notice.I think i duration should be equal from either side
They are asking me to give 3 months notice which is applicable to confirmed employees.
If there is any specific clause related to Probationers,then that should be applicable of any general condition for 3 months notice.

dear
legally bank is worng.appointment letter is a civil contract and terms should be same from both sides .the above said contract is void abnitio.
if they terminate one month pay and if u go three month pay not justified as well as legal.
condition can be three month notice during probation also but it has to be from both sides.
tks
j s malik

Can you quote some rulings to substantiate my position? Some legal document or some Govt of India guidelines.i really don't understand how come a public sector bank can issue illegal unjustified appointment order ? They say that its bank's policy and fighting the case in civil court will be quite a daunting task.if i can get some sort of document which could tell them that sticking to unequal terms is illegal then that will help me a lot.