I don't understand your statement.
Do you believe a thorough investigation has not already taken place?
Yes, I believe a thorough investigation has not already taken place. For one thing, there have been reports, nowhere contradicted, that Zimmerman was not tested for substances and that such tests are standard practice. For another, the initial report has him arrested (or detained if you like, or charged in a preliminary manner) with negligent homicide or manslaughter (I saw that on the pdf of the police report); and for such a charge one might reasonably expect a more thorough inquiry than has been described in all reports. For another, one witness claims that she had to persist in requests to give her statement; when a death has occurred, I do believe the police should not have to be asked twice to hear from a witness.
Yet another reason: the police are virtually certain to be sued by Martin's parents, and therefore they have an obligation to produce a very thorough investigation indeed. They'll be called to account for every minute detail, commission and omission.
Also, just about everyone here -- everyone fair and reasonable -- has admitted that we don't have sufficient facts. I'd venture to say that is at least partly because a thorough investigation was not done.
By the way, I don't hear Zimmerman's lawyer claiming that no further investigation is necessary. If that were the case, surely he'd be saying so.
Question you didn't ask: do I think an investigation, grand jury proceeding or the like would now be conducted impartially? No, I don't think it would. The case has gone political, befouled with racial politics.