No, you will not require contraception after removal of the ovaries as you will not be ovulating and therefore you cannot fall pregnant. 

However, keep in mind that you are still able to contract many sexually-transmitted infections or diseases. Talk to your doctor about which barrier methods are most suitable for you.
​

Visit www.iapmd.org/surgery for lots of evidence-based information and resources for those considering, going through or recovering from surgery for PMDD/PME.