The court had deferred hearing on the bail application
What sentence went before this? I ask, because I am trying to understand why you are using past perfect tense.
Do you mean it was originally set for Tuesday, but deferred; or deferred, and reset for next Tuesday?
The chances are very bleak
'prospects' may be bleak, but I think the better choice of word is 'slim' or some such.
that the court will remand Dr. Rajesh in (the-omit) police custody
as Police do not have evidence with it.
as there is insufficient evidence.
The police had arrested Dr. Rajesh, a dentist, for allegedly killing his 14-year-old daughter, and domestic help.
Without the comma, it reads as if his daughter had the role in the home of 'domestic help'. The comma makes it a little clearer that there are two people ...but 'for allegedly killing both his .... , and domestic help.' makes it crystal clear.