Immelt claims the company's state taxes have increased five times since 2011 and the new budget would impose "significant and retroactive tax increases for businesses." GE—which employs more than 5,700 people in the state—started to consider the move "after a lot of thought and in the context of our ability to compete," he said.
"I believe we should pay our fair share and that all of us should give back to our communities. But, we can compare Connecticut with other states where small and large businesses have a better environment to thrive and compete," Immelt wrote.
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Connecticut Gov. Dannel Malloy noted Thursday that he would consider revising some tax provisions amid backlash from GE and other employers. The state's top Senate Democrat, Martin Looney, suggested GE was using its budget criticism to mask already planned layoffs.
GE told CNBC that Lonney's assertions were "completely untrue."
Malloy's office did not immediately respond to CNBC's request to comment.
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— The Associated Press contributed to this report