Can I start baby siiting with play group in my home without getting permission. Is there is any rule for before opening baby sitting we have the permision. If yes please explain me in details

Nope, you need serious official permission to do this type of activity.
Difficult to tell you what exactly as it varies by location.

Please start with what country you are in, and what state or province etc.
Generally the answer will be that you need a license and liability insurance, and you won't want to risk it anyway. If something happened - illness, injury, death, abduction, charges of abuse or crime - think of the consequences. But the law will depend on where you are.

Large difference between doing some baby sitting and operating a day care. In the US each state has rules, and if you are normally watching children on a regular basis you have to meet state guidelines including food handling, equipment and more.