"Szukasz tamtej kobiety?"

Translation: Are you looking for that woman?

[IE99]

Is this genetive singular? If so, why not the accusative, kobietę? Thanks

[immery]

Yes it is singular, genitive.
Because you need genitive after szukać.

(My interpretation - because NIE MA JEJ , and we need to JEJ SZUKAĆ,) - as you probably know negation usually needs genitive

[BarnacleWes]

What about "you are looking for that woman"?

[Jellei]

As the Polish question didn't use 'czy' - yes, the indicative word order is also a good interpretation. Added now.

[MarzenaRok]

It's all right to but lady instead of women or not?

[Jellei]

Well, "lady" is not a basic word, while "woman" and "kobieta" are totally basic...

Also, "lady" isn't even as popular as "pani" in Polish.