I'll post this here for reference, and put a reference to this forum post
as well, just for fun
I recently applied for the Certificate of Clearance (CoC, formerly known as CNCC = Certificate of No Criminal Conviction), to apply for residency in another country (planning to leave here before things get really weird). Not being Singaporean, the "official" answer of course is that you cannot have one. The unofficial answer is, no problem, but you need to make two personal appearances at the Police Cantonment Complex.
At first I thought I could just get it at a neighborhood police station, what with Singapore being all networked, but no dice. I followed the instructions of another post I found online (and the police officer), and it worked out well (at least, so far).
First thing to do is to walk to the Police Cantonment Complex on a weekday, between 8.30am and 11.30am (or was it 12.30pm, maybe). The earlier the better, I should think, although there wasn't much of a queue when I went. You need to bring your passport (and PR card if you are PR, I think), and at least another photo id (other than your PR/EP), since you need to leave one at the entrance for the visitor id. You will also need a letter from the place where you are applying for visa that states that you need this CoC (in my case, with a copy of my EP attached). Additionally, two passport photos are needed. Ideally, you should also bring copies of the passport and the visa letter.
There is an airport-style luggage scanner and metal detector gate after you get your ID, so don't bring a lot of metal or any weird things.
On the second floor (lifts on the left after the scanner), there is the small office for getting the CoC with a queue number system. In my case, there were not a lot of people, so I filled out the form first. There are forms there for Singaporeans and non-Singaporeans to fill out, so pick the one you need and proceed to fill it out - it is several pages, and a bit repetitive. This already includes (for foreigners) the appeal form. Date of leaving should be the submission date. I got the queue ticket once I had finished filling out the form, and was called up less than 5 minutes later. The forms for foreigners are not available online btw, the only place to get them is at the PCC.
Once it is your turn, the officer will take and check your paper work, make copies if needed, and ask for payment of the S$45 fee - NETS, Credit Card or Cash (exact change). After that, it's back to waiting for getting your fingers scanned - that took a while in my case. All 10 fingers will be scanned.
The processing time is 3 weeks (recently increased from 2 weeks, it seems). I am currently waiting to pick it up. Pick-up has to be in person if you are in Singapore (or can send somebody on your behalf, with a signed letter of authorization) at the PCC again, from 9am onwards, and requires (apparently) the payment receipt. They do send it by mail, but only to addresses outside of Singapore.