The process is online now. Its called a COC - Certificate of Clearance.
How to apply:
1) Go here -
http://www.police.gov.sg/e-services/apply/certificate-of-clearance
2) Select "Appeal by non-citizen to apply for a certificate of clearance"
3) Log in using your FIN
4) Follow instructions and file your appeal. You would need your passport and digital photo, and your ITA to be submitted as proof of why you need a COC.
5) Once the appeal is approved, go back to step 1 and select "Apply for certificate of clearance"
6) A simply acknowledgement from your end, payment of $55, and then submit.
7) Once approved, go back to step 1 and select "Book a fingerprinting appointment"
8 ) Select a time slot and submit
9) You will have to go the Police Cantonment Complex (Right above the Outram Park MRT) and provide your fingerprints, during the time slot you selected.
10) You will recieve the COC the same day, within a few minutes of providing your COC
Let me know if you are stuck anywhere. The entire process may take around 4-6 days or even more.