I am not a lawyer but in the US I believe once the verdict of not guilty is given the state is done. For example the oj Simpson case. Almost everyone agrees he likely did it but the jury gave the verdict not guilty because, according to interviews after, the state didn't provide enough evidence. They can't go back and say "sorry our lawyer was bad at his job, let's do a new trial". He was released and didn't face any criminal charges for the murder. Fun fact the Kardashians initially got famous/rich because the original father was one of oj's defense attorneys. Now they family of the victim later sued for emotional damage and won and he was also later arrested for other crimes but the criminal case of him killing his wife could/can't ever go back on trial.