The Italian Tsunami Warning Centre (Centro Allerta Tsunami, CAT) of Istituto Nazionale di Geofisica e Vulcanologia (INGV) operates to issue tsunami alert messages both to the Italian Civil Protection system and to several countries of the Mediterranean. CAT-INGV started its activities as a candidate tsunami service provider in the framework of the ICG/NEAMTWS of IOC-UNESCO in 2013, to become operational in 2016. At national level, it operates since 2017 following the "SiAM" Prime Minister Directive, under the coordination of the Italian Civil Protection Department and together with ISPRA. In this paper we discuss the responsibilities of the CAT-INGV operators in the light of the Italian legal system, describing which are the critical aspects of the surveillance and issuance of the alerting messages, and trying to delineate the tools useful to limit legal problems for the operators in case of damaging events or false alarms.