This is serious and its pathetic that the police wont help. You can easily set up a Keylogger SQL Php Code to track IP's but that might be hard. (I can do this method for you, just send me the other persons email to mine at limitedgenius@live.co.uk and I will get the person's details for you)
OR, you can try these steps which most commonly work 40%.
Check the sending email address to see if you recognize it. Sometimes, people send emails with fake or anonymous names, but forget to change their sending email addresses. In this case, you can easily determine who sent your "anonymous" emails.
Look at the header information on the email. This is disabled by default in most email browsers, but can be viewed easily with a few quick menu selections. In Outlook Express, for example, go to the "View" menu and click on "Options" and you should see an option for viewing full headers in an email.
Scan through the headers to look at the xheader information next to "Received:" There should be two such lines, the first from your own mail server and the second from the originating mail server. In some cases, you will find that this second email server is a domain you recognize, and the sender of the email can be deduced.
Check the IP address in the xheader next to the second "Received: from" line. Even if you don't recognize email addresses and servers, IP addresses are rarely masked. The actual IP address used by your email's creator should be right there for you to see.
Look up the IP address using the tool in Resources. This will give you all the public information for the registrant of that IP address, which may allow you to deduce who is sending you anonymous emails. (Then you can ask the police to narrow the location down to one person)
Hope this helps! Choose as best answer for writing all this in 10mins! :)