Not necessarily. Ultimately it depends on the fundamental reason that generates the crash, but usually the opposite will happen.
Bitcoin is a store of value that doesn't relate to any country in particular, so if your country's currency falls, people are likely to buy BTC the way they would Gold. As an example, recently my country's currency fell quickly when the media reported incriminating evidence against the President, and in a matter of minutes the price of BTC relative to it went up by ~30%.
If that seems like anecdotal evidence, the same thing happened with the US dollar when Trump fired the FBI director. The Dollar fell to the lowest since the election, and meanwhile Bitcoin increased in value and hasn't gone back.
Does BTC correlate with other currencies, specially the USD? Yes, but it's not tied to it. It's like the USD/EUR market; sometimes both currencies may go down for the same reason, or both may go up, but usually one will gain value relative to another because they're independent.