Translation:My friend introduced his sister to me.
Mój przyjaciel przedstawił mnie(accusative) swojej/jego siostrze (Dative)
I do not know if you already know it , but swojej here means his ( of the friend that introduced me/her); while jego means his ( somebody else's)
I really think this sentence needs 'to' before 'his sister'. And then it's exactly like it was mentioned in the comments above.
Yes. "to" is needed for one or the other of the two persons. Just like the need for the Dative in Polish.