No, if you dont have the domicile of Tamil nadu then you cannot apply for the same. To make it more clear below I am providing the eligibility criteria for Nativity of the applicant, please go through it-
1. Domicile residents of Tamil Nadu should have qualified 8th, 9th, 10th and 10+2th standard in the state.
2. If the domicile residents have completed their 8th, 9th, 10th and 10+2th standard from outside the state, then they will also be eligible provided they bring their copy of nativity certificate.
3. Children of government employees whose parents have been serving the state for the past 5 years from the day of application will also be eligible even if they are not domicile residents.
4. The children of All India Service Tamil Nadu cadre officers will also be termed eligible for admission.
5. If the applicants parent have been working in public sector or government recognized institutions for the past 5 years from the time of application, then they will also be eligible for admission.
6. Non resident applicants of Tamil Nadu will also be considered eligible for admissions provided they have completed their 8th, 9th, 10th and 10+2th standard in the state. These applicants will not have to submit their nativity certificate.
7. Under the category of open competition, the Sri Lankan Tamil refugees who have completed their studies in Tamil Nadu will be eligible for admission if they are able to submit their identification certificate from the Head Quarters Tahsildar.

To know more about TNEA eligibility criteria, you can go through below article -

TNEA Eligibility Criteria 2017


Good Luck!!!