Shami tree is worshipped and the leaves of Shami tree are exchanged among each other in some places of India.
Shami pooja is known as Banni Puja or Jammi puja in some South Indian dialects.
Here is the Shami Puja stotram:
Shamee Shameeyathe paapam
Shamee shatru vinashanam
Sri Ramasya priyadarshineem !!
Amangalanaam shamaneem, shamaneem dashkruthasya cha
Dusswapna nashaneem dhanyam prapadyeham shameem shubhaam //
Shami shamiyathe papam shami lohitha kantaka
Dharithri arjuna baanaanam ramasya priyavaadini //
Karishyamaana yatrayam yadhakaalam sukham mayaa
Thathra nirvighna karthrithwam bhava sri rama pujithe //
Chanting or reciting this prayer even once on Dasara would bring you prosperity and success in coming year.