Notice period depends on your employment terms. Some Company follow one month notice and some follow 3 months notice. Please check your appointment order.
If you have any dues pending to be recieved from your past employer, you can request them to adjust the same towards shortfall in notice period. If not, visit your HR by person discuss with him/her and close it amicably and get relieved properly.
You may not require the relieving certificate based on current scenario, however tomorrow the situation may change and you may be required to submit a proof of past employment with your future employer. If you leave this issue unattended your past employee proceed with disciplinary proceedings warning/termination process wherein your personal file will be closed with remarks absconded/unauthorized which will not be good for you.
2nd July 2019 From India, Madras