I don't know anything about WA law, but that is ridiculous. I'm not sure what the police department's definition of "due process" is but as a general rule it means fairness and a meaningful opportunity to respond to the charges. Of course you are entitled to your police report! Now, they may be able to stall until your arraignment date (first court appearance) but not your trial date!
Contact a local experienced criminal defense lawyer ASAP - s/he will educate the cops on due process.
I practice here in Bellingham.
You ARE entitled to your police report(s). There is a process, however.
(1) You won't obtain police reports from the police department. Period.
(2) If you are represented by a public defender or private attorney, then they will obtain your police report.
(3) It's harder to get your police report quickly if you represent yourself. Generally, you can review/read your police report before entering a "Not Guilty" plea at your arraignment. Show up early. Request the report from the prosecutor (know that at this point, you cannot copy it; nor can you leave the room with it). Enter your "Not Guilty" plea and inform the court and prosecutor, on the record, that you wish to represent yourself "pro se," and you want your police report. This puts all parties on notice. Underestand, however, you may not obtain reports until your pretrial/omnibus date, which is given at arraignment. But you will eventually get them.