A Florida woman smashed through a gate near President Trump’s Mar-a-Lago estate, bizarrely claiming she thought it was a “car wash” — sparking a police chase that ended with her pit bull being shot dead after it bit an officer, according to officials.

Alexa Rae Scharf, 29, drove into a closed Secret Service checkpoint near the sprawling Palm Beach property Tuesday evening, parked her vehicle beside the screening tent, got out and turned on a hose, according to an arrest affidavit obtained by CBS 12.

When a Secret Service agent there asked her who she was, Scharf strangely replied, “I’m here for the car wash,” according to the affidavit.

While…

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