Not only do you have valid concerns, the situation obliges good parents to manage it appropriately. However you are way off base on one point which I'll mention below.
First what should be obvious: You cannot, and should not, try to dictate the terms of your ex-wife's life. Not just because it's futile and wrong, but because it would almost certainly make things worse.
Do maintain good lines of communication with your ex. Treat her like a good friend and be considerate of her life and feelings. This is an investment. It will benefit your child in a lot of ways over time. Specific to your question, it makes it easier to gain insight on how the situation is unfolding.
Pay close attention to how shes responding to the environment, how her personality evolves and any changes in behavior. If it's all benign, then great you should be paying attention anyway.
Wrong thinking to be cautious of:
This "give people the benefit of the doubt" crap in the comments is wrong and dangerous. It's a virtuous thing to do most of the time, but when a child may be left alone with a new adult it's absolutely correct to error on the side of caution. The fact the guy is probably harmless is irrelevant. Say the odds of him mistreating her are only 1 in 10,000. You just can't ignore risk when the stakes are so high if there's a practical way to mitigate it. Risk of driving a car maybe you can't avoid, but this is different. Find out whatever you can about him and don't feel bad for a second.
[he's a] policeman, and so theoretically is safe to be around children
This is so wrong you are scaring me. Without condemning cops, why would you think they are better in their personal lives than the average person? Secondly, I hate to mention the worst case but sexual abuse has come from every respectable, prestigious, honorable career you can think of. Again he is probably a great guy but without knowing that yet, someone's career choice should give you zero additional confidence about the safety of your kid.
On commenters saying 'how would you feel if someone checked up on you': How we should feel is that we should not give a rats ass about a perceived slight when someone tells us they are taking good faith precautions regarding safety of the most important thing on the planet. Of course this should be done with as much consideration and respect as possible. But if you are going about it right the right way and always being polite, then don't even bother worrying about what he thinks.