From what I've heard, there is some racism in Ukraine.
The police are more likely to stop and ask for documents dark-skinned, foreign-looking people.
Here is a travel warning from the U.S. Department of State for U.S. citizens travelling to Ukraine:
"In addition to incidents of assault, persons of African or Asian heritage may be subject to various types of harassment, such as being stopped on the street by both civilians and police officials."
http://travel.state.gov/ukraine.html