As of version 17, libpq is always reentrant and thread-safe. However, one restriction is that no two threads attempt to manipulate the same PGconn object at the same time. In particular, you cannot issue concurrent commands from different threads through the same connection object. (If you need to run concurrent commands, use multiple connections.)
PGresult objects are normally read-only after creation, and so can be passed around freely between threads. However, if you use any of the PGresult-modifying functions described in Section 32.12 or Section 32.14, it's up to you to avoid concurrent operations on the same PGresult, too.
In earlier versions, libpq could be compiled with or without thread support, depending on compiler options. This function allows the querying of libpq's thread-safe status:
PQisthreadsafe #Returns the thread safety status of the libpq library.
int PQisthreadsafe();
Returns 1 if the libpq is thread-safe and 0 if it is not. Always returns 1 on version 17 and above.
The deprecated functions PQrequestCancel and PQoidStatus are not thread-safe and should not be used in multithread programs. PQrequestCancel can be replaced by PQcancelBlocking. PQoidStatus can be replaced by PQoidValue.
If you are using Kerberos inside your application (in addition to inside libpq), you will need to do locking around Kerberos calls because Kerberos functions are not thread-safe. See function PQregisterThreadLock in the libpq source code for a way to do cooperative locking between libpq and your application.