Q: If a piece of evidence was inadmissible at the time of arrest can the prosecutor bring it in at arraignment?

A: The concept of "admissibility" only pertains to evidentiary hearings and trials. An arrest is not an evidentiary hearing or trial. There is no judge or jury to consider the evidence. You can view "admissibility" as whether something is "admitted" for consideration by the judge or jury in making a final determination of some matter.

At the time of arrest, law enforcement can and should collect all of the available evidence and preserve it for consideration by the court at later evidentiary hearings and trials. If a particular piece of evidence is inadmissible, the defendant can object at such a hearing or at trial, stating the reason why. The judge then has to decide whether that item is or is not admissible.

A defendant might decide not to object for tactical or strategic reasons, in which case a judge can and most likely will admit the item into evidence. For example, a particular piece of evidence might "cut both ways" providing both information that is favorable for the prosecution and information that is favorable for the defense. A particular piece of evidence might be inadmissible in the form that it is offered--hearsay of what another witness said or an uncertified public record--but, with additional time, could be presented in a different form that is admissible--the eyewitness himself testifying or obtaining a certified copy of the record; in which case, a defendant may prefer not to have a delay in the proceeding particularly if they are in jail and unable to get a bond to secure their release pending trial. The defendant is said to have waived any complaint that piece of evidence is inadmissible.