Hope you are staying safe! I will assume you mean inpatient hospitalization for psychological difficulties.
As far as I know (and information current as of 6 Oct 2020), NUH, SGH and Sengkang Hospital have very limited beds.
Also, it will depend on the cause of your symptoms.
For example, if it was found that a brain infection or an autoimmune condition was causing a patient's emotional difficulty, I believe the public hospitals will be able to accept the patient as long as the patient's emotional difficulty is not disruptive to the ward or the nurses are capable of taking care of them.
Nevertheless, if you believe you or your loved ones are in immediate danger of self-harm or harming others, kindly seek medical attention.
Travis