Without knowing your specific situation we can't decide. The general answer must be: the DNS who is authoritative for the IP. Who is responsible / autoritative is stored at the RIPE. And as Luciano posted, the responsibility can be delegated.
On the other hand, if you run a DNS in your LAN with your own private domain, then of course your DNS reverse resolve the IPs, as long as you configured not only a forward zone but a corresponding reverse zone too.
Alexander
What it boils down to is this, we have Network Solutions as our primary DNS servers so we don't use our ISPs for handling our DNS records. I want to bring our primary in house but my boss is terrified that if out T1 goes down we are screwed. Well, yeah if it goes down our site's not up so why would our DNS be so important. We need to be able to reverse DNS for the email we send to be sent properly.
Make sense?
-- Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt.
Mark Haney Network, Database and Systems Administration DoctorDirectory.com Inc.