A friend of mine is going for a city management position dealing with big budgets. She has many years of Human Resource & Insurance background and has dealt with budgets. But she knows that her personal credit is a mess and is worried that the city will run her personal credit as part of their background check. I personally think it’s a violation of privacy. Her past work experience shows she can deal with her work budgets, it’s just that she screwed up in her personal life. Please let me know! Thanks 
Yes they can. The state permits certain type of employers (which includes your friends), to pull Credit reports for a number of different reasons:
* Credibility. Does your personal financial history indicate a completely different type of pattern, in terms of responsibility, than your entrusted job position?
* Liability. Are you only taking this job because you need money and might want to just pay off debt then abandon ship?
* Character. You're applying for a reputable position, does your personal credit show grossly irresponsible decisions that might make you untrustworthy as a person?
All these questions are what employers are looking to answer when high-risk job positions are being given to prospective employees. For my job at a bank, they actually ran my Credit right in front of me. I was offended!
It's all about risk these days, as in, no one wants to take on any. Unfortunately, it IS a bit intrusive to say the least, but it's state and government permitted and it serves as a great advantage to an employer.
If it's any condolence, keep in mind that not all employers are simply looking to see whether or not she has bad credit. They might be looking for specific things such as bankruptcy, judgments against her over $5,000, etc. The "serious stuff", not just being late on every bill she's ever received.
If they are checking her Credit and it's loaded with serious negativities, she probably won't get the job. If it's smaller stuff, she has a chance.