I've been told by a girl supposedly from New York I met online, who currently is working in Ghana, that she requires police and medical reports to return to the US.
Is this true? The cost was quoted at $570.
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First off I believe you are being scammed. Being Ghanaian and American, having had extensive interactions with the American Embassy in Accra, and having lived in Ghana for decades, I have some knowledge on how these scam artists operate and it smells like a fish and stinks to the high heavens once money is being demanded from you either subtly or directly.
Now it is possible that the airline which will transport the said citizen is requesting medical clearance before it does so, perhaps because of some contagious self reported disease like tuberculosis or like during the Ebola outbreak a three years ago.
There are many documented incidences of US citizens being deported from the USA or being denied entry into the USA, however this is in cases where their citizenship is in dispute. Once confirmed though, USA immigration law gives all citizens the right to enter.
The Fifth Circuit in William Worthy, Jr. v. US, 328 F.2d 386 (5th Cir. 1964):
We think it is inherent in the concept of citizenship that the citizen, when absent from the country to which he owes allegiance, has a right to return, again to set foot on its soil.
US government can also put a suspected terrorist on a no-fly list such that although citizens have the right to return to the USA at any time, any airline would not allow them to board. In such a scenario it is not a police certificate which is going to clear them.
The Congress provided the President of the United States, in section 212(f) of the Immigration and Nationality Act (INA), with the authority to suspend the entry of any class of aliens the president deems detrimental to the national interest. This authority has been exercised by nearly every president since President Carter, and has been a component of immigration laws since the enactment of the INA in 1952
However despite all these disclaimers, I can say with an extremely high degree of confidence that you are being scammed. It may be that he/she is the scammer, or that she/he is in league with the scammer, or that she is ignorant and being scammed herself although the chances are much higher for #1 & #2. There are ways to test to detect whether you are dealing with a scammer however I believe stackexchange is not the place for such. Do a simple Google research and you will get good information.
Sounds like a romance scam (the setup described by the OP is very similar to the point of being indistinguishable from Nigerian scam, 419 Scam)