I'd like to help, but this is kind of gibberish: "the law states that all marital assets must be acknowledged and notorized by both parties." What law? "acknowledged and notorized by both parties"? Huh?
The remainder of your question sounds like you're saying that a trial date is approaching and there hasn't been asset disclosure that you're satisfied with. This is what the "discovery" process is for - you (or your attorney) should have supplied each other with full Case Information Statements, then sent interrogatories, notice to produce documents, etc., and, if unsatisfied with the responses, should issue subpoenas (or can issue those earlier, in advance of voluntary discovery being supplied). Depositions are occasionally appropriate to review the discovery and explore whether everything has been disclosed.
Most cases don't require this level of litigation - most of the time, the parties know what's there and any gaps are filled in when the CIS is filled out. If you think money was hidden, you need to pursue this aggressively. If a trial date is approaching and the case is approaching a year old, you may have a problem - if you're not represented, it's past time to get a consult. If you are and there's been no discovery undertaken, it might be time for a second opinion.
The above is said without seeing your case file and without my understanding the entirety of the facts of your case. Depending on those facts, the above information be may incomplete or may be completely inaccurate. The above is intended as general information only based on what you described and not as legal advice. I advise you to consult with counsel who may be able to provide better information commensurate with a better understanding of your situation.
In most cases, the judge may use their discretion to make any ruling they deem appropriate under the circumstances. Whether this is true in your particular circumstances cannot be determined from your question, and should be answered by a local attorney after review of the specific facts and circumstances pertaining to your case. You can search the attorney profiles here on Avvo for an attorney in your area. Good luck!
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If the other party is hiding assets, your attorney must make a motion to compel compliance. If they insist there is nothing else, you must provide some evidence that there are more assets he is not disclosing.
If one party does not sign the Property Settlement Agreement, then the case is set for trial.
The responses to questions here are not legal advice, as the facts are very limited.
In some important respects your question does not provide sufficient information. The rule of law and our system of justice is premised on the notion of notice. In only the most extreme and rare circumstances, predominantly in criminal law, will one party be permitted to retain information to the exclusion of the other. I can think of no time when that would be acceptable or permitted in a divorce. The Judge however is the final arbiter of these decisions.