They could, given the facts as you have expressed them. However, they might not. You never know.
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It is possible, though not certain from the limited facts you present, that the police could develop probable cause to believe that evidence of a crime could be found in your home. In that case, they could get a search warrant. It would be best not to keep anything incriminating in your home.
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If they sell it right to whatever judge is on "warrant duty" for the week, they could possibly get a search warrant for your house and computers. I would error on the side of caution and be concerned that they would and make sure that you do not have anything incriminating readily apparent.
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With a warrant, police can search your home anytime.
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It's possible, but since it was 3 months ago, they may have trouble convincing a judge that there's probable cause to believe there's evidence of a crime at your residence now, based on those facts alone. However, you can't be too cautious. If there's something you wouldn't be proud of in your house, or on your computer, get rid of it. Odds are if the contents of the bag are determined to be contraband, you'll be arrested and charged with possession. If you're in your home when they serve the warrant, the officers can do a safety sweep and any contraband in plain sight can be used against you.