Defamation of Character

I was recently subjected to defamation in our office. Here's what happened:

A subordinate of mine requested for an extended leave due to family emergency. The day that she's supposed to report for work, she did not show up but our manager received a resignation letter via email. The reason for resignation was apparently because of me, being a bad boss and a power tripper. As her accusation is without any basis, I was able to clear my name. My HR manager sent the ex-subordinate a reply email acknowledging the resignation but she has to report back to do clearance and exit interview. 2 days after, she replied to the email denying that she was the one who sent the resignation letter. She also sent me a personal message through social networking site that she did not do it but I should be careful of the people around me and told me to watch my back. That was the last time we heard from her, she never returned to the office and she is now considered awol. A few more days after, I received three e-mail threats from different senders ("Mamamatay ka din","Isa isa lalabas ang baho mo", "Lalayuan ka ng tao sa paligid mo"). We were able to trace the emails and there was one email which was sent from within our office. I was also able to hear personal accounts from several colleagues and I am pretty sure of who's involved in this issue.

My question is, do I have a case to file? Is there a 'demand/complaint' letter that I can send the ex-subordinate to summon her to return and explain her side?

you will first have to prove who sent the email and do it with certainty. maybe your IT guys can determine who did it. on emails, usernames and/or IP addresses are the standard of proof.

if you are able to pinpoint who did it, you can try to argue that the mamamatay ka din is a threat, but it sounds more like unjust vexation to me.

i would be careful about how you communicate with the subordinate unless you have proof that she is the one who sent the emails. unfortunately, anonymity on the net has been a refuge of such cowardly acts.