Sure you can. You can "plead the 5th" in any context at any time. The only requirement is that you have some basis for believing that your testimony may tend to incriminate you. A common misconception is that this means you actually have to be guilty of some crime but the "incriminate" in this context simply means to make it more likely that you would be prosecuted for a crime. The Supreme Court has affirmed that the 5th Amendment's privilege against self-incrimination exists, in part, to protect innocent men who otherwise might be ensnared by ambiguous circumstances. Accordingly, it would defeat the purpose of the protection if you could only use it after you had been charged and put on trial.
To build on your example, let's say you witnessed that car accident because you were out taking a late night walk - something you ate earlier was keeping you awake. Coincidentally, a house down the block was robbed that night and the police are looking for a perpetrator based on a description that could easily fit you. You had nothing to do with the robbery but you don't have a verifiable alibi for the relevant time period either. When called to testify as a witness in civil litigation regarding the car accident, you would be entitled to plead the 5th because going on record to declare that you were in that location at that time might make it more likely that you could be prosecuted for the robbery.
