There are private psychiatrists practising at Mount Elizabeth Medical Centre, Gleneagles Medical Centre, Novena Medical Centre and other private facilities. You can call up the clinic and arrange for an appointment to see the psychiatrist.
If you decide to seek treatment from a private psychiatrist, then there is no strong need for you to get a referral letter from the polyclinic. However, if you have other medical problems and are taking medications for various medical problems, it will be good for your treating physician to write a note to the psychiatrist so that the psychiatrist can understand your medical problems better. There are potential drug-drug interactions and the psychiatrist can then avoid prescribing antidepressants that may interact with your existing medications.
You can also approach your general physician for a referral. Referrals from the general practitioners to the restructured hospitals are treated as private cases.
Yes, it is possible to seek treatment from the restructured hospital as a private patient. The advantage of going in as a private patient is that you can select the psychiatrist whom you want to consult.