Yes but they will likely lose. In order to win the cop would have to show that not only did the person make a false statement but that they knew it was false. The person would likely say 'I remembered it happening differently' and that would be that in most cases.
Isn't it funny that a cop can sue us for defamation but a cop can illegally arrest us, make up charges, plant evidence, cost us a ton of money for bail and fighting the charges and often times we either lose or are forced into taking a plea deal out of fear of a much longer jail sentence but a jail sentence nonetheless and a felony jacket to boot.
They can do all of that to us, it has happened untold times and continues to happen to this day literally ruining lives and most of the time we can't sue them personally. In the very rare case that we are allowed to sue them personally the taxpayers almost always cover their legal costs. They can even get qualified immunity if they aren't certain if what they are doing is illegal (ignorance of the law) which lands us normal plebes in jail. Even if they get caught red handed the vast majority of the time the absolute worst that happens is they lose their jobs and sometimes that doesn't even happen.
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