One suspects this film registered better with viewers in 1943 than it does today. Despite being suggested by the actual assassination of Reichs Protector of Bohemia and Moravia Reinhard Heydrich, better known to the Czechs as "The Hangman" because of his excessive brutality in dealing with residents of the conquered regions, it is almost total fiction. Even so it is not bad as a rather involved drama and was very likely good anti-nazi propaganda.
Perhaps it is well to start with what actually did happen to Heydrich on May 29, 1942. Two young Czechs, Jan Kubis and Josef Ganchik, parachuted in from an RAF plane and managed to ambush "the Hangman" riding in his open Mercedes. Armed with both machine pistols and a bomb, the apparently did little harm by shooting, but did explode the bomb under the car. Heydrich's spleen was penetrated by bomb fragments and debris causing death several days later, possibly more by infection than anything else. The two Czechs evaded capture briefly, but witnesses under torture revealed their hiding place in a church and the SS killed them. In a massive retaliation, Hitler picked the village of Lidice, more or less at random, from among places known to harbor anti-German sentiment, and ordered its total annihilation. The people of Lidice had nothing whatever to do with the assassination, of course.
In HANGMEN ALSO DIE we have the story of a lone assassin, using an English made pistol, whose getaway taxi was forced to move by German soldiers, causing him to take refuge during the curfew at the home of a Czech professor. The professor's daughter, Mascha, had impulsively directed the German pursuit away from him. The German police suspect the girl, but release her in the hope she will lead them to the wanted man. They also round up many Czechs, including the girl's father, and begin shooting them as hostages. The girl at first intends to give information, hoping to save her father, but in the end is persuaded otherwise by the Czech resistance. A plan is concocted to bamboozle the SS and save the assassin and the girl, but what it is you will have to see for yourself. Be assured it is incredible.
As you see, this story has little to do with the historic assassination and its aftermath, beyond illustrating the SS brutality, but it does make a mildly entertaining wartime adventure with good propaganda value, largely because of the rather low key, intensely personal nature of the plot elements. Some of the characters are very real and believable, e.g. the Gestapo Inspector Gruber, the girl Mascha, and her father, all ably portrayed by Alexander Granach, Anna Lee, and Walter Brennan respectively. On the other hand, some characters are more like cardboard cut-outs and get wooden performances to suit. Brian Donlevy as Dr.Svoboda, the assassin, fits this category alas, as do a number of others. What realism there is seems likely to have been the contribution of Bertolt Brecht rather than John Wexley, who got the credit for the screenplay. One likes to think that Fritz Lang did the best he could with a mixed bag of acting talent, but this can hardly be said to be his best effort.
Just why Hollywood producers seem to prefer fiction to the facts when dealing with historical material is a major mystery to me. In 1943 the general facts of the assassination were known, if not all the details, and could have made just as dramatic a story as this fictional one. It is worth a watch, though, especially if you like Anna Lee.