When does a doctor feel that a person who is suffering from depression should be admitted in hospital

Unless the depression encompasses some other symptoms that would endanger others, then I don't think he would admit the person to the hospital. Depression can usually be treated successfully with medication.

There's no rule or set guideline, but in general it's when you are 'harmful to yourself or others.' That's the term used for calling the police/ambulance or holding you in a hospital.

It might be any of these:
When you can't promise to tell the doctor about suicidal thoughts and plans.
When you claim to not be able to stop active thoughts of suicidal thoughts with plans.
When you cannot function even at home with daily routines of bathing, eating, sleeping, keeping the utilities running and the house safe.
When you find other people at home unbearable and do something to harm them or yourself.
When you engage in self-destructive behavior, whether overdosing, self-mutilation like cutting or burning, or risky acts socially (walking dangerous streets at night, driving too fast, sex with any stranger, drugs and alcohol).
When you believe that forces are beyond your control or people are out to get you.
Each doctor makes his or her own determination, of course.
Many have lost patients to suicide, and they are human too, so their decision will be somewhat individual.