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At a certain point in the story, the detective finds a letter from one of the suspects (who is the director of a play,) which is intended to intimidate one of the other suspects (who is an actress in the play) so she won't talk about something that the lead actor of the play did to her. The director of the play was worried that if the secret about what his lead actor did to the other actress, the play would be cancelled/destroyed.
Currently, the way the detective finds out is through searching the actress' house and finding the threat, but I was wondering if there was a more creative way to do it.
Sure. Round up the usual suspects. What you select depends on your plot and your tolerance for cliche. Of course, writing a detective story requires at least a medium level tolerance for cliche. Anyway:
Instead of finding the letter by searching the house, the detective gets invited for superficially legit reasons, and the letter is apparent, or seen after a mini-search. Say, on his way to the bathroom, he passes the desk of the actress and pulls open one drawer and there it is.
Third party brings it to the detective. The maid or makeup artist or photographer. Variations abound. The third party can be helpful, jealous, a blackmailer, hates the actress or the director or both, or loves same, etc.
These days it could be an email or text message instead of a paper letter. Variations on how the detective got hold of it are many. From a clever 12 year old helper to the grizzled old hacker to the director or actress being clueless about security, etc.
The director is compulsive about records and has kept a photocopy of the signed letter. The detective searched the director's home or office. With variations as with searching the home of the actress.
Various pratfalls, accidents, and coincidences. The actress has the letter in her purse and there is an accident with it that spills the contents. Or the detective stops a purse thief, and during the scuffle the contents are spilled. These events can take place in a setting that gives the detective the correct amount of time to look at the letter, either a brief glimpse or he gets to keep it, etc.
The director is arrogant and believes the detective is powerless. He brags about the letter. Possibly to a henchman when the director does not know the detective is nearby. Or even directly to the detective.
There are tons of other variations. The letter is fake, written by the actress, and she needs it to be seen to forward her plot. The director and the actress have some other scheme going, and they need to appear as enemies. The secret in the letter is bad but the actress has some worse secret, so she exposes the letter to deflect from that worse thing. There are many many other possible scenarios. And each of these could be hinted at to keep the reader from the final solution.