I am a landlord in CT. I have a tenant on a month to month with no signed lease at this point. We have both acknowledge a month to month verbally, via email records and by paying a monthly rent for 18 months.

She just gave 7 days notice on the first of the month and expects me to prorate her rent for the 8 days of the last month she will be in the house; therefore she expects a majority of her last months rent back that she had paid when moving in. I am under the belief that she must give 30 days notice on a month to month which she did not. Also, on a month to month, if she spends 8 days of the month in the apartment, then she pays the month. Am I correct? She is theatening to report us to the housing authority--but does she have a "leg to stand on"? (Our states website only says "proper advanced notice".)

If it is a month to month lease and she only spends 8 days in the apt. and hasn't given you 30 days notice, then yes, she has to pay for the 30 days.

Yes, if this is a month to month verbal agreement, she has to give a month ( 30 day) notice. So let her threaten you, laugh at her and tell her she obviously has no idea of the law.