Constance, I would say very safe during the day but at night time you need to look out for certain places like the zähringerplatz where weird people are often around, but overall, there are not many people outside at night time, especially in quiet regions but near the center and in public transport, you should stay aware anyways. 

Constance is generally a very safe city. How ever during night when walking home it does happen that some drunk guys catcall you and in my experience the police isn‘t very helpfull for women in dangerous situations. But i guess thats a general problem, not only in constance.

Constance overall is super safe, especially going out for women by night is not a problem. You can walk through the oldtown and the other parts comfortably! Only be aware of bicycle thiefs as there are quite some 😅

Rather small city in Germany with safe neighborhoods and well lit streets. I have never felt unsafe as a woman even at late night hours. City center is small, very walkable and petty crime is very low.