Idiom Request – Is There an Idiom for Perfectly Fitting Clothing?

(Note that piece of painting isn't normally idiomatic in English.)

A very common idiomatic usage in this context is:

The police chief asked "Does this painting ring a bell?"

ring a bell (also ring any bells)
to sound familiar

Don't take that sound too literally though. The expression can just as well be used in contexts where it might be directly replaceable by ...seem, look, smell, taste, feel familiar.

In much the same vein there's also touch / strike a chord, which could (just about) be used in OP's context. But that one often has stronger allusions to strike / hit home which usually conveys particularly, often painfully relevant. As in His story about being mugged struck a chord with me (because I myself had been mugged, so listening to him brought back disturbing memories).