The suspect's parrot, which is known for screaming at midnight, woke up the entire building.
The neighbor who called the police was wearing a superhero onesie.

Use which (not that) for non-defining relative clauses—the ones separated by commas that add extra, non-essential information about a thing or animal.

Use who as the subject pronoun for people in defining relative clauses. (Whom is used for objects, and which is used for things).