They can't just withhold evidence and give it to you right before trial. There is a discovery period and the state has to turn it over. Discovery would include any written statements that the police took from a witness. Sometimes there is a lag and judge's are pretty liberal down here about giving the state time. As far as statements go, its up to your attorney to either depose or speak to the state's potential witnesses prior to trial.
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This is a complicated question that raises many issues. The police can prepare multiple reports. In fact it is their duty to prepare more reports if they get new information. The duty to provide discovery is an ongoing duty of the prosecutor. If the police or prosecutor (considered one unit for purposes of discovery violation analysis) willfully fails to turn over discovery in a timely manner and it prejudices the defense, it can result in exclusion of evidence or, in some extreme cases, dismissal of charges. As my colleague mentioned, most judges are liberal in giving the State breaks and extensions, for political reasons, but there is a limit.
Witness statements are some of the most crucial discovery and must be disclosed. If there is no statement your lawyer should take a deposition. Even if there is a written statement, your lawyer may want to take a deposition, particularly if you face serious charges.
One last thought, you have a constitutional right to a speedy trial and constitutional right to due process (discovery). Florida appellate courts have repeatedly said that defendants must not be forced to choose between one fundamental right or another. If the State discloses late stuff that would cause a defendant to either have to "waive" his right to a speedy trial to review the new stuff and change his defense or go to trial unprepared to keep his right to speedy trial intact,, the defendant is faced with a Hobson's choice and the State may be forced into a dismissal.
Smart prosecutors get discovery to defense lawyers in a timely and efficient manner as they do not want to end up on the wrong side of one of these types of issues and facing a very angry judge.
One additional thought. I just noticed you said the witness is a CI. The State is entitled to withhold the identity of a CI if they do not intend to call the CI at trial. If a defendant then wants to learn the identity of the CI they defense must file a sworn motion alleging grounds as to how the CI may be material to the defense (such as entrapment, etc.). These motions are usually granted if facially valid.
If the CI is a necessary trial witness then he/she should have already been disclosed and any statements provided, by this stage in the proceedings.