At a high level Indian citizenship can be acquired in 3 ways:
- By Birth
- By Descent
- By Registration (aka Naturalization)
At the time of the birth of your child, they are a citizen of India by descent. For this however you need to register the birth of the child with an Indian mission within 12 months of their birth. I know that you've said that you've chosen not to go down this route but I'm mentioning this as this may be helpful to someone else in the same position.
These are the documents needed to register the birth with the Indian mission:
- A copy of the birth certificate of the child
- A copy of the Indian passport of both the parents
- A copy of the certificate of Indian citizenship if acquired by registration/naturalization
- A copy of the marriage certificate of the parents
- Declaration letter that the child does not hold the passport of any other country
The key part here is that the child must not hold the passport of any other country in this case, the USA at the time of the registration of the birth.
After registration of birth, you can then apply for the Indian passport of your child. The key document that you need here is a copy of the registration of birth document that the Indian mission gives you from the previous step.
After acquiring the Indian passport of your child, you can go ahead and then apply for an American passport. Do note that a minors passport is only valid for 5 years at a time and you will need to renew this every 5 years. And when the child turns 18 then they will need to either renounce their foreign citizenship or Indian citizenship. In general by acquiring foreign citizenship the individual is deemed to have lost their Indian citizenship, however the issue is that a minor cannot renounce their Indian citizenship.
This is the route that I have personally taken and my child holds both an Indian and American passport.
Now getting to your particular question, the short answer is yes your child is eligible to acquire Indian citizenship by registration. These are the list of required documents -
- A copy of valid Foreign Passport of the child or parent or which has/ her name is entered
- A copy of valid Residential Permit/LTV
- Proof of Indian citizenship of both the parents’ viz. copy of the Indian passport, birth certificate, etc.
- In case of guardian, enclose proof of guardianship
For Item 2, A copy of Residential Permit you can use the OCI card for your child. You can apply for an OCI card after first obtaining their American passport.
In this case too, the child can't renounce American citizenship till they attain the age of majority (18) at which point they must choose to remain and Indian citizen or to not.