It depends entirely on the basis of citizenship.
This is correct, in some
cases the person will be asked to provide proof of renunciation of their other citizenship, but not in every case.
not also polish requirement
This is incorrect - it is case specific, see below examples.
Claiming Polish citizenship exclusively on the basis of Polish ancestry: renunciation of other citizenship is always required
Applying for Polish citizenship to the President of RP (regardless of reasoning): In most cases renunciation of other citizenship is required.
Foreigner being recognized as a Polish citizen on the basis of having lived in Poland for a certain length of time and met other conditions: In most cases renunciation of other citizenship is not required.
I know people that have gone through each of the above cases (including myself) so I know what I am talking about through actual