The eligibility claimed during online registration, is subject to document verification for the respective eligibility criteria.So, you do need to carry your Eligibility certificate in KEA NEET PG document verification.You aslo need to carry your secondary school passing certificate as a proof of your date of birth. Along with these documents you also need to carry :

NEET PG Admit Card and Score Card issued by the NBE

Karnataka PG medical 2019 application form with the payment receipt

Photo ID Proof (Aadhar Card/PAN Card/Driving License/Voter ID/Passport/Ration Card)

Two passport size photographs which should be same as uploaded by the candidate while filling NEET PG 2019 application form.

MBBS year-wise detailed mark sheets

Compulsory Rotating Internship Certificate

Provisional internship completion certificate for candidates who will be completing their internship by March 31, 2019.

An undertaking on Rs. 20 Stamp paper needs to be submitted for Karnataka PG medical admission 2019.

I hope this helps .If you need any further information on this you can refer to the following link:
https://medicine.careers360.com/articles/karnataka-pg-medical-admission