Will the DA still try to prosecute even though no bodily harm was done to that woman?

My husband was jailed and charged with assault with a deadly weapon because he heard me arguing with a woman who was harassing me for a parking spot and basically started to follow me to my residence. He ran to see what was going on and this woman looked at him and yelled that he had a knife which was not true. It was his cell phone. I was present the entire time and so was my mother. The cops did not question my husband. Instead, they slapped handcuffs on him and took him and later confessed to him that the charges won’t stick since no weapon was found.