Singapore fundamentally does not provide PCC's to non Singaporeans. But, they can on technical grounds. All you have to do is apply with an appeal form along with a demand draft, application form and the photograph.
Are you applying from within or outside SG? If you're in SG, it's fairly easy, fill out your documents and go there in person and give your fingerprints. If you're outside, it's more complicated. I applied for a Singaporeean PCC from within Japan and it took me well over a month to get it.
Also, you will need some sort of a document. As previously mentioned, try taking the ITA letter and see if it works otherwise you're going to have to ask the CIC agent to provide you with a formal letter once you're applying for your PR.