NO! It is NOT needed automatically.

The injection is needed ONLY if the baby has positive blood (if you and your DH are both Rh- then baby is also Rh-: this is a recessive gene, you'd need the baby's dad to be Rh+ to give the baby a chance at being Rh+ too) AND there is a situation where your bloods could mingle, such as if you fall and land on your tummy. Even then it isn't a given.

Don't accept anything like this "just because". It's actually a blood product so could contain all sorts of hidden nasties. It isn't even necessarily needed after birth; get them to check your blood for antibodies first. I had a VERY unprofessional midwife who refused to tell me the results of this and just gave me the injection - in fact, there were no antibodies found in my system immediately post-partum.

I'm against needless injections, btw. Just thought you may not have picked up on the bias LOL.