Termination of Employment Contract: No notice period stated in offer letter

I tendered my resignation in a company where I have worked for almost 1 year as a junior executive. However the notice period was unknown as it was not stated clearly in my offer letter. The offer letter only asked me to refer to the employee handbook, which I asked HR for a copy but he said that the company does not have such handbook and I were to email him personally if I have any questions regarding HR. I stated a 1-month notice on my resignation letter but my employer mentioned that the notice period is 3 months instead. I checked all the documents I have but there is no such statement in black and white. I checked with the labour department and they said that my notice period should only be 1 month based on my work duration. In addition, my employer fails to pay EPF to all employee's accounts. Is what my employer doing correct? Otherwise, what should I do? 

@ yeemei

employee handbook
As this term refers to HANDbook.
It is just a book that was handed to you only for reference only.
Even if you sign on a copy, it has no legal reference as it normally covers a very wide and broad spectrum for various categories  of job functions /jobscope and their restrictions. The main legal contract of service is the signed Employment Contract / Appointment Letter between both the employer and employee before one joins or started work on the first day.

notice period should only be 1 month based on my work duration.
The labour Officer is correct. The minimum is thus when there is no clear indication of the termination period  stated in the contract. The minimum, thus, follows the minimum requirements as stated in the Employment Act 1955.

Is what my employer doing correct?
Based on your above declarations
1. The employer is bullying you as a newbie in the workforce

2. Failure to make contributions to KWSP can command a jailterm and heavy fines.

How to punish these type of people?
Come back here after you have left the company.