If an employment contract expires, shld notice period be served?

Last year, I joined an organization as a Consultant on 13/Aug/2014 on contractual basis. The employment contract had a validity of 1 year i.e the contract expiry date was 12-Aug-2015. In the contract, a point was mentioned that either party can terminate the contract by giving 1 month notice period. There was no mention of auto-renewal in contract. On 1/Aug/2015, I gave a letter to HR stating that I do not wish to renew my contract further. As the contract was expiring on 12/Aug/2015, I decided to leave the organization on 12/Aug/2015 itself and verbally informed HR about the same. HR accepted my letter and made no effort to retain me or start the process of contract renewal. Also, HR did not mention about 1 month notice period at that time. On 12/Aug/2015 i.e. on my last day when I approached HR for clearance and experience certificate, HR denied to provide experience certificate. HR told me that as I've not served the complete notice period of 1 month, I need to give them salary of remaining 18 days of notice period to get the certificate. As there was no way to convince HR, I spoke to higher officials of the hospital. They assured that they'll resolve the issue but finally no one helped. Till date, > I've sent a letter and an email to HR requesting them to release the experience certificate and 12 days of my salary > Also, I've received a letter from HR stating that I've to pay for 18 days to get experience certificate and 12 days of my salary. I would request you to review the case and provide your suggestions. Thank you.