"I do not see a woman."
Translation:Nie widzę kobiety.
Not entirely sure but I believe "Nie widzę kobiety." is for when you're speaking about yourself not seeing the woman whereas "Nie widzi kobiety." is for when you're speaking about another not seeing the woman. As in, "[Ja] nie widzę kobiety." - "I don't see the woman." and "[On/Ona] nie widzi kobiety" - "He/She doesn't see the woman."