You can use the Tees Valley Indexes website to check whether Middlesbrough Register Office holds the record you're looking for. If you find the record you need, make a note of the reference number and quote it when you're ordering your certificate.
Please note, the Tees Valley Indexes website also holds records for Redcar and Cleveland district. If the record you need is held by Redcar and Cleveland, you'll need to order a copy of the certificate from the register office for Redcar and Cleveland.