Greeting Sudha,
Suicide in a work spot can certainly put pressure on the Management on one hand. But on the other hand she is your employee and she certainly needs counseling. Mr.Dinesh has suggested the center and in my opinion I would recommend that you take her through this process.
If you have good rapport with the local police station, you can inform them. However, if they insist that you have give a letter in writing, you may have to abide by it, as you have the obligation to protect the interest of the Management as well. But I am sure that police authorities do not harass suicide cases.
In the meantime you can consult the respective department head and give the employee time off from work, to avoid any unpleasant situations immediately within the organization.
You have to certainly alert the parents, if required in writing about the happenings and advise them to support their daughter in the counseling process.
Regards