We consider a memoryless Erlang loss system with servers
= {1, …, J}, and with customer types
= {1, …, I}. Servers are multitype, so that server j can serve a subset of customer types C(j). We show that the probabilities of assigning arriving customers to idle servers can be chosen in such a way that the Markov process describing the system is reversible, with a simple product form stationary distribution. Furthermore, the system is insensitive; these properties are preserved for general service time distributions.