Here are different studies on false rape accusations:

https://en.wikipedia.org/wiki/False_accusation_of_rape#Rumney_(2006)

Of all of these, I want to focus on this one by Kanin:

https://en.wikipedia.org/wiki/False_accusation_of_rape#Kanin,_USA_(1994)

In my view, this is the best study on false rape accusations. All accusations were investigated by authorities, an offer for a polygraph was given, and it was only counted as a false accusation if the accuser admitted it was false. The fact that they were all investigated with an offer of a polygraph makes it seem like the best method to me. Yes, I know there is some controversy about whether polygraphs are actually valid (they aren't allowed in court after all), but many people see it as a valid tool regardless.

The results found that 41% of women admitted their accusations were false when going through this method. The actual rate is definitely higher than that, since there's no way all of them admitted to it.

Of course, feminists have criticized this study, but they haven't provided any methodologically superior study as far as I can see. Any studies they point to have problems and don't take the steps Kanin took.

I'm not saying this one study proves everything. More studies with his methodology will have to be done to be even more sure. But it's not to be dismissed either.