She alleged that the permission for the Shah's road show was given by "withdrawing Section 144 (prohibitory orders) in the area by the new Commissioner of Police appointed by the Election Commission".
Violence had broken out during Shah's road show in the city on Wednesday and the statue of Ishwar Chandra Vidyasagar was vandalised inside a college, named after the social reformer.
"The roadshow was itself a deliberate, intentional, and a criminal conspiracy to vandalise the culture and heritage of Kolkata and West Bengal and also to defame the West Bengal government and its people," the letter said.
Banerjee also alleged that West Bengal has seen "a number of illegal, unconstitutional and biased decisions during the election process because of undue influence of the Central government and ruling party at the Centre".
"As a result, not only the state administration and its officers but also the common people of the state have been harassed and attacked in various manner," the letter said.
She urged the commission to ensure that the election is completed "peacefully, impartially, and without any undue interference of the Central government and without any intervention by the ruling party at the Centre".
Banerjee also requested Arora to protect "democratic institutions and federal structure of the country and extend due respect to the opposition parties".
She also alleged that the commission had appointed two retired government officers - Ajay V. Nayak and Vivek Dube - as special observers "which is not in accordance with the law".
"These two special observers had shown partisan attitude and always complied with the instructions given by the Central government and the ruling party at the Centre time and aagaisn. All these issues were brought to the notice of the Election Commission of India but no justice has been done," she said in her letter.