There are several ways to do this. Do you really need a whole post type for People? You could do this as a custom taxonomy and assign it to the Press Release post type.
You could create a custom user role, and then utilize that to assign an “author” to each Press Release.
If you want to keep everything you have now as is, your best bet would be to create a custom meta box, which populates a select field with all of the “People” listed in it. Then save it using update_post_meta()
You could also utilize the post_parent field and assign the ID of the “People” post to it.
As you can see, there are several options. Perhaps others have more.