Conn. Gen. Stat. § 12-251

(b) The rate of tax on gross earnings of railroads shall be fixed as follows: (1) When there is no net railway operating income, or the net railway operating income does not exceed eight per cent of the gross earnings, two per cent of the gross earnings; (2) when the net railway operating income exceeds eight per cent of the gross earnings, but does not exceed ten per cent, two and one quarter per cent; (3) when the net railway operating income exceeds ten per cent of the gross earnings, but does not exceed twelve per cent, two and one-half per cent; (4) when the net railway operating income exceeds twelve per cent of the gross earnings, but does not exceed fourteen per cent, two and three-quarters per cent; (5) when the net railway operating income exceeds fourteen per cent of the gross earnings, but does not exceed sixteen per cent, three per cent; (6) when the net railway operating income exceeds sixteen per cent of the gross earnings, but does not exceed eighteen per cent, three and one-quarter per cent; (7) when the net railway operating income exceeds eighteen per cent of the gross earnings, three and one-half per cent, provided with respect to the tax under subdivisions (1) to (7), inclusive, when there has been filed with the Governor by the Commissioner of Transportation the annual certificate of eligibility for exemption required by section 13b-232 with respect to the year ended said thirty-first day of December, there shall be no tax on gross earnings but a fee of twenty dollars shall be paid to the Commissioner of Revenue Services with the statement required by section 12-250 . The amount of taxes paid during the year ended said thirty-first day of December, in any town in this state, on the real estate not used exclusively in the business of such corporation, or of any corporation all of whose property is operated by such corporation, shall be deducted from the amount of the tax upon such gross earnings.

See Secs. 13b-226 to 13b-233, inclusive, re standards of service required to maintain exemption.