Legal Question in Criminal Law in Massachusetts

The police can testify about statements made by the defendant just like any other witness. The weight given by the jury to the testimony of the officer can be effected by lack of miranda statements, etc.

The administration and waiver of Miranda warnings impacts the admissibility of the alleged statement. However, Miranda is only required when the suspect is both in custody AND subject to interrogation; things that the person said but not in response to any question are not subject to Miranda.

As for the lack of a written signed statement or audio/video recording of the alleged statement, the absence of a writing or a recording goes to the weight of the evidence but not to it's admissibility. The police can testify that the person made the statement without having to produce a writing or a recording.

Note that voluntariness, or lack thereof, of the statement is another separate but related prerequisite for the admission of a person's statement.