There are probably as many procedures for escheatment as there are institutions that perform the function. Some good resources in this regard are National Association of Unclaimed Property Administrators at www.naupa.org
and the Uncliamed Property Professionals Organization at www.uppo.org.
Also, going to each state's unclaimed property site to read their rules and regs can help to determine what you need to put in place.
At a basic level (very basic), escheatment will involve 1) identifying dormant properties, 2) attempting to locate the owners through due diligence, 3) compiling a report of properties that remain after the due diligence, 4) filing a report with the jurisdiction, and 5) retaining documentation based on the jurisdiction's requirements.
This is primarily a backoffice function, but branches do be come involved when customers respond to due diligence or when researching accounts for signature cards, dates of death, not transactional contact, etc.