Well she said she couldn't found anything about her birth at the hospital. This has two possible explanation.
Either she was born outside of the hospital/village or her records has been deleted by someone with authority.(Kakashi, Naruto and Sakura comes to mind)
If she born outside of the village, it is possible that Karin is her mother and died during child birth. Maybe she overused her healing ability which spent most of her life-span. Now I find Sasuke having an affair with Karin is impossible, he shown no interest in her. Suigetsu once said that Karin done something with Sasuke's DNA or something, maybe she done something like a test-tube baby by using Sasuke's DNA which she obtained. But she died during child-birth and Sasuke brought the baby to village where Sakura adobted her. There is a lot of what ifs in this 'theory' of mine but i have a feeling that it is something like this.