Está is the present he/she/it/you formal form of the verb estar, which is one of the verbs for "to be". When está precedes a verb, the following verb will end with -ando if it is an -ar verb or -iendo if it is an -er or -ir verb.
Tú estás nadando (You are swimming)
Estoy corriendo (I am running)
Therefore, the correct answer is "El culpable está mintiendo," dice el señor juez.
