Actually, many Caucasian-majority cities have a non-Caucasian mayor and or police chief.
For example, back in the old days here in Los Angeles, the city was still predominately Caucasian, but the people elected an African American mayor who served for 20 years.
They wanted to prove how unprejudiced they were. His name was Tom Bradley, a retired cop.
He was considered a moderate, so the voters felt that they could trust him. He ran for governor of California, but he lost even though the polls said he would win. Experts say that people who were polled simply chose Mr. Bradley because they wanted to prove how liberal they were but changed their minds inside the voting booth.
New York City has a terrible mayor who is Caucasian, but the city is rife with non-stop violent crime.
So if one is seeking a city where the crime rate is low, one should not judge it by the ethnicity of the mayor or police chief.