Muslim Law

It's Hindu.

The child can be a Hindu or even a Muslim, whatever her mother decides according to the Hindu Minority and Guardianship Act, 1956. 

The Supreme Court in the case of  Gita Hariharan v. Reserve Bank of India and Vandana Shiva v. Jayanta Bandhopadhaya, the held that under certain circumstances, even when the father is alive mother can act as a natural guardian. The term 'after' used in Section 6(a) has been interpreted as 'in absence of' instead 'after the life-time'. -

Rights of guardian of person. -The natural guardian has the following rights in respect of minor children:

(a) Right to custody, .

(b) Right to determine the religion of children,

(c) Right to education,

(d) Right to control movement, and

(e) Right to reasonable chastisement

These rights are conferred on the guardians in the interest of the minor children and therefore of each- of these rights is subject to the welfare of the minor children. The natural guardians have also the obligation to maintain their minor children.

So, according to clause (b), the mother, who is a guardian has the legal right to choose her child's religion.

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let the child explore it by his own tell him/her the complete detail about the religion hindu and muslim you can enrolled your child in Islamic summer school which give the proper information about Islam.