The first is correct:

I have heard that many people died in this apartment.

Informally we might say, I've heard many people died in this apartment.

The second uses the past perfect. It is well explained here and you can test yourself.

The first is correct:

I have heard that many people died in this apartment.

Informally we might say, I've heard many people died in this apartment.

The second uses the past perfect. It is well explained here. And you can test yourself.