In the US, Yes, generally
In the US an accused can, in most cases, be convicted on the testimony of a single witness, who can be the victim. There are a few exceptions.
Article II section 3 of the US Constitution provides:
Treason against the United States, shall consist only in levying war against them, or in adhering to their enemies, giving them aid and comfort. No person shall be convicted of treason unless on the testimony of two witnesses to the same overt act, or on confession in open court.
The case of United States v. Wood, 39 U.S. 430 (1840) states as a general rule that a conviction for perjury cannot be based on the unsupported testimony of a single witness:
In Russel on Crimes and Misdemeanors 544, it is said,
"The evidence of one witness is not sufficient to convict the defendant on an indictment for perjury, as in such case there would be only one oath against another."
A second witness or supporting documentary or circumstantial evidence was required. However, the court in Wood analyzed the rule and its exceptions at some length, and concluded that documentary evidence, at least when the documents were written by the accused himself, and showed the existence of a conspiracy, of which false statements under oath were a regular part, was sufficient to support a conviction without any witness who testified to the falseness of the accused's sworn statements. The conclusion was:
[It is] the opinion of this Court that in order to convict the defendant of the crime charged in the indictment, it is not necessary on the part of the prosecution to produce a living witness if the jury shall believe the evidence from the written testimony sufficient to establish the charge that the defendant made a false and corrupt oath...
(The case in Wood involved an importer who, according to the government, falsely swore to overly-low values for imported goods, so as to reduce the customs duties payable. A series of letters from the importer to his partner in the scheme in England was accepted as proof. No testimony about the actual value of the goods was presented, but the conviction was upheld. I am not sure if, more than 170 years later, the rule from Wood is still valid law.)
In an article dated 2018 from Time "Here’s Why ‘He Said, She Said’ Is a Myth" the issue of sufficient testimony in cases of rape and sexual assault is discussed. The article says:
Under old English law, rape prosecutions could not be brought unless every material element of the victim’s story was corroborated by another witness or evidence. Because sexual assaults don’t usually happen in crowded pubs, this rule effectively barred many cases. Victims of any other type of crime — muggings, robberies, physical assaults — could provide the sole testimony at trial. Rape victims were uniquely excluded from the criminal justice system.
...
The corroboration requirement lasted for hundreds of years and became law in the United States. It blocked the prosecution of most rapes. For example, a study in 1969 showed that New York City’s corroboration requirement resulted in eighteen rape convictions out of 1,085 arrests. An outcry in the 1960s and ‘70s caused many jurisdictions to reconsider their requirement, leading to some notorious debates.
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New York abolished its requirement in 1972. Today, most jurisdictions have deleted their corroboration requirement.
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When Arizona prosecutor Rachel Mitchell wrote in a memo after questioning Dr. Christine Blasey Ford at the Brett Kavanaugh hearing that a “‘he said she said’ case is incredibly difficult to prove,” she neglected to mention that a sex-crimes prosecutor’s very job is to go beyond the parties’ contradictory statements to find evidence suggesting whether “he” or “she” is telling the truth.
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What’s striking about the Kavanaugh case is that the evidence we saw at the hearing was more significant than what is presented in many criminal trials where a guilty verdict is returned. Dr. Ford’s credible testimony, her statements making this accusation years earlier, and her lack of motive to lie, especially compared to the incentives for her to stay silent, would be legally sufficient to sustain a criminal conviction for attempted rape.
Thus convictions for rape and related crimes are now routinely made in the US based primarily on the testimony of the victim, often with supporting circumstantial evidence.
