Baby's dual citizenship

Ana

Hi everyone! I was wondering if anyone knew the process for a baby to have dual citizenship. I'm Argentinian and my fiance is American. In Argentina the process of making my baby American is long and complicated, so we figured it would be easier for the baby to be born in America and giving her my Argentinian citizenship, but I can't find any information online regarding this process. Does anyone know how it works? is it automatic? (if I just show them my passport at the hospital will they also write her down as Argentinian?) or do I have to go through paperwork to get it done?