That's why I was wondering if at that time we had кати́тся and where I could find such an information.
If you are looking for a diachronic analysis of Russian stress in general, the most comprehensive work on it is Andrey Zaliznyak's От праславянской акцентуации к русской (1985).
Poetry in accentual-syllabic verse (силлабо-тоническое стихосложение) is one of the primary sources of this information (of course, only covering the relatively brief period of time when it was a thing).
The first book that systematically addresses Russian orthoepy, Русская Грамматика by Alexander Vostokov (1831), already lists ка́тишь as a verb with a mobile stress pattern. Both крути́шь and верти́шь mentioned in the other answer are listed as having the fixed stress pattern (unlike now).
However, the vast majority of poems (although not all) written before 1840 use the stress on the inflectional ending (кати́шь). By 1870, the use of this pattern in poetry significantly declined, and by 1900 all but disappeared.
Otherwise, what are the rules of classical Russian poetry allowing such rhymes?
Accentual-syllabic verse, as the name suggests, puts a constraint on the stress pattern (the rhythm) in addition to the one on the sequence of syllables (the meter). Such verses should use stress patterns close to the ones generally used by speakers in prose, although small deviations are tolerated. If you are reading a poem in accentual-syllabic verse (virtually everything written after 1770), there is a good chance that the rhythm of the poem reflects the actual stress pattern of the word as of the time of its writing.
This is opposed to the earlier syllabic verse, which only paid attention to the meter and tolerated the deviations in stress to a much greater extent. Reading poetry in syllabic verse takes a lot of getting used to, although they do use the rhyme as well.
One of the most prominent authors of syllabic poetry in Russian was Antiochus Cantemir.
