Legal Question in Constitutional Law in Maine

Who is doing the searching here - the police or the employer?

It is not clear from your question, but it seems like the search was done by the employer, and not by the police.

The Constitution provides some protection against "unreasonable searches" but that restriction on searching only applies against the Government (state or federal). A private party (such as, I assume, your employer) is simply not subject to the Constitutional restriction, at all.

If the employer did the searching, then your question is not really about Constitutional law, but about an invasion of privacy, or possibly trespass, which are civil causes of action under state law.

While there is no general right of an employer to make this kind of search, just because of the employment relationship and nothing else, there could be some additional facts that establish a legal privilege to search, that the employer is exercising. For instance, the company might have a published policy in your employee manual that authorizes it and you implicitly agreed to this policy when you were employed.

If the car were parked on Company property, that might also be a factor.

It's hard to tell from your question, but it seems like the car might be a "Company car" rather than the personal car of the employee. That would make a difference and also if the Company is providing cars in this way, it may very likely also have written policies about searching the cars that it owns, policies that you may have (wittingly or unwittingly) agreed to.