There are several "services" that you can send emails through. You send it to the service and they forward it to the recipient without revealing your email address, so that you remain anonymous.
borked.net is possibly the best known of these.
As a personal observation, I see no evident legitimate reasons for a service of this kind; but those who provide the service claim that there are some.
Several of them have cooperated to some extent in revealing sender identities in response to investigations by legitimate law enforcement agencies, especially where identity theft, threats, or abuse are apparent. They generally have the capability of providing the necessary information; but can only provide it to "appropriate authorities" when it's requested "in proper form," since they risk suits and/or prosecution for "failure of privilege of personal information."
The problem is with getting a legal authority to assign a sufficient priority to an individual complaint to actually get an investigation launched, as such investigations can be astonishingly expensive and difficult to prosecute to any useful end result.
In areas where I've seen complaints proceed, it's seldom that a complaint to local police appears, although a very few local cop shops do have "internet offense" specialists. A County Attorney's office is more likely to have the resources, and if there's no response there most State Attorneys General have at least some "lip service" internet crime offices that might be helpful.
Internet Crimes can also be reported, in the US, to the FCC (Federal Communications Commission) which has the Federal regulatory burden for interstate communications in general, although I haven't looked for some time to see what "complaint input points" are on their website.
Using an interstate communication system for the purpose of transmitting a threat or to attempt abuse of a person is a crime that can be prosecuted by the FCC. In "international crimes" there is some cooperation between countries, and a couple of convictions, crossing national boundaries, have occured for simple theft of a few bucks worth of music downloads.
The actual making of a threat, or the accomplishing of abuse is a crime that probably falls within the jurisdiction of the FBI to investigate, and is within the jurisdiction of the Office of the US Attorney General to prosecute. Both have "internet crimes" offices, but getting an individual instance investigated may be difficult, since they're generally pretty busy with mass/serial offenders.
Usually it's necessary to show evidence that more than a local (within a single state) abuse is actually involved, but in some cases the fact that an "interstate capable medium" is used may be sufficient to invoke Federal assistance.
1. Complain to local police, since other authorities may request evidence of this complaint as a condition for considering your complaint to "higher authority" and/or for taking action.
2. Complain to County/Parish Attorney, since the County Attorney is much more likely to have someone assigned to work such complaints.
3. Complain to the US District Attorney for your jurisdiction, because the DA is most likely to be able to forward to agencies you'll need assistance from to get an interstate investigation launched.
4. Check for a website where you can file an FCC complaint appropriate to this kind of offense.
5. Check back with each of the above after a reasonable time for advice on what recourses are available to get something to happen.
6. DOCUMENT WITH DATES, TIMES, AND PLACES all communications that may be evidence of what's being done or that show actions you take in response and results of the abuse you claim has occured.