The man had reportedly barricaded himself inside the cinema complex.
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Man opens fire inside cinema complex in Germany; injures nearly 50
Gunman reportedly held hostages, barricaded himself inside
She was shot dead by the elite forces, reports said.
Police shot the man dead after elite forces stormed the complex, the Mannheimer Morgen newspaper reported, citing the interior minister of Hesse state.
The Darmstaedter Echo said 20 to 50 people had been wounded.
But Bild daily said that according to police, about 25 people were hurt because of exposure to tear gas.
Earlier, Focus Online magazine reported that German police had arrested the man.
Police were not immediately available for comment.
Several media reported that the man had entered the cinema complex at around 3 pm local time (1500 GMT). The Frankfurter Allgemeine said it was unclear if there was a political or ideological motive or whether it was a robbery that went wrong.
© Thomson Reuters 2016
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