Charging the association of "gross mismanagement", Amin pointed out that GCA has not even submitted its accounts to the Board of Control for Cricket in India (BCCI) for the last two years which has deprived it of latter's annual grants.
He demanded that poll dates for GCA election should be announced immediately.
Countering the allegations, GCA secretary Rajesh Patel said, "GCA is functioning well. We will get our accounts audited and hold the elections next month. Some people want power and so they say such things."
State chief minister Modi had become the head of the premier cricket association after defeating Congress leader Amin in the September 2009 election.
Levelling further allegations, Amin said the Central Board of Cricket Ahmedabad (CBCA), an important component of GCA, had also not submitted its annual accounts for the last four years while AGMs were not held for the last three years.
Amin said the CBCA president and secretary had issued a press release in July promising to conduct polls in September. But its constitution says that elections have to be held before September and fifteen days prior to polls, an AGM has to be called.
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Objecting to inclusion of Venugopal Rao and Saurashtra's Rakesh Dhruv in Gujarat's Ranji Trophy team, Amin said the move would affect emerging talent from Gujarat in getting into the playing eleven.
Three teams - Baroda, Saurashtra and Gujarat - from the state participate in the Ranji Trophy. While Gujarat Ranji team is governed by Gujarat Cricket Association (GCA), the Baroda Cricket Association and Saurashtra Cricket Association look into the affairs of Baroda and Saurashtra Ranji teams respectively.