。
She seems to have some connection to the case.
Literal
She [topic-は] that case [with-と] something [genitive-の] connection [subject-が] exists seems.
と here marks the standard against which a relationship is measured ('connection with that case'). 何か ('some, some kind of') hedges the connection — vague but real, refusing to specify what kind. 関係がある ('have a connection / be related to') is the positive counterpart of 関係がない. ~ようだ adds inference: based on observable evidence, this seems to be the case. The whole reads like a detective's tentative conclusion or a journalist's careful framing — short of an outright accusation but pointing strongly.