Bismihi ta'ala
This is a bit of a complicated question, because it can be looked at from various angles.
Assuming that the question is asked by a woman living in a non-Islamic country.
We will have to consider a few scenarios that would occur and will determine whether she is able to overcome these situations, from a shar'i perspective.
Will she be able to observe her correct hijab, and modesty, along with her other religious obligations, like salat, sawm, etc.
As a police-woman, there could be situations where she will have to freely mix with non-mahrams, like a non-mahram male police partner, and that could be a problem.
There would be situations where she will have to physically handle a man, and if it not emergency cases, then that could also be a problem, from a shar'i perspective.
Will she be enforcing something that is legally lawful, but religious prohibited. That is going to be an issue as well.
What if she chooses to work a desk job, and not patrolling the streets, for example? In this case, she also needs to look at whatever scenarios that could arise, and decide whether it is suitable for her or not.
Yes, we understand that in every occupation there are going to be challenges, and shar'i matters that a woman, and even a man, must take into consideration when they choose their career path. However, that being said, it is always best to be realistic and find something that one will be comfortable with and also represent their deen in the best way possible.
Personally, I believe we Muslims in the West do need female police officers, not just for the purpose of showing that a Muslim woman can be in the work force, but so that she can contribute in educating her colleagues more about how the Muslim community is. But of course, as long as it does not clash with her religious and family commitments.
And Allah knows best.
