No, but ...
Australia does not have the concept of "pressing charges" but police and prosecutors have guidelined discretion over whether to bring charges.1
In new-south-wales the guidelines involve answering two questions:
- can it be said that there is no reasonable prospect of conviction on the admissible evidence?
- is the prosecution in the public interest?
Whether the victim is cooperative or not impacts on both questions.
For question 1, the prosecution is required to consider "whether the prosecution witnesses are available, competent, compellable and reliable" (my emphasis). An unwilling witness may give non-committal answers like "I don't know" or "I can't remember" which don't help the case and fall well short of perjury.
For question 2, the prosecution is required to consider "the victim’s attitude to a prosecution", "the victim’s age, physical health, mental health or cognitive impairment and whether the prosecution may have an adverse physical or emotional impact on the victim", and "the protection of the victim and the victim’s family". A victim that does not want the trial to proceed weighs against prosecution.
However, the consideration of the second question is not the victim's interest, it is the public interest including such things as "the seriousness, or conversely, the triviality, of the offence", "the prevalence of the offence in the community, whether it is of considerable public concern and the need to denounce and deter the offending behaviour", "the accused’s criminal history and background" and "whether the offence occurred while the accused was serving a sentence, on bail or remand." Prosecution (or not) may be in the public interest even if it is not in the victim's interest.
1In Australian jurisdictions the police act as the prosecutor for summary offences with the case being brought by a uniformed officer carrying out the role of "police prosecutor". The Director of Public Prosecutions has the responsibility for pressing the case in indictable offences. Very roughly these correspond to the US distinction between misdemeanours and felonies. A summary offence is one that has a maximum penalty of imprisonment for 2 years and some indictable offences can be tried as summary offences which limits the penalty to that maximum.