Miss Gauri,
First of all i would like to congratulate you for success of your hardwork and pray god that in future you will certainly fulfill your dreams with your hardwork and blessing of parents and the almighty.
You should not disclose your new appointment on either of the side and should resign first with any other reason and get relieved off your duties from the dept you are currently working in and then join the new one and also should not disclose the experience in your attestation form in new dept.
In a nutshell, whatever you do no one on either side should know that you are doing. Everyone does like that. even at the time of police enquiry you should say that you were not working anywhere and your neighbours who will be witness they should be adviced to pretend the same.
this is my experience, but you will have to take decisions carefully after all this will be your decision and you'll be responsible.
I hope my advice will work take your decision.
Your Friend