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The answer is yes, they can refuse. But if they do, ACS may try to go to Court.
Understand that ACS has no "power" per se. They cannot force an interview, and they certainly cannot simply take a child away from the parents without a a court order. However, they have a mandate from the state to stand in front of the Court for any child that they feel is being abused/neglected.
This means that if they feel that the child is neglected/in danger, ACS may decide to take the matter to court and ask to have the court agree that your parental rights should be suspended (or even terminated in serious scenarios) until you show to the court that you are an able parent (such as mandatory drug tests for a while and drug classes). Now, while ACS has the "ear of the court," this does not mean that the court always agrees with ACS and if you challenge their claim, it may be denied. But this is a risk.
If ACS sees an issue, they will normally request that you to take an action (such as a drug test and if positive, then a drug class) and if not, then they can approach the court and the court may agree that if you do not, you'd risk ACS going to court to ask for the same.
If you feel that the requirement by ACS is unreasonable, then you can refuse. If they then go to Court (as explained above), then you'd have to show that your decision is in line with "best interests of the child."
ACS often uses misleading, cajoling, and threatening tactics, so be careful. An attorney is recommended if one decides to meet with them, because the attorney can quickly cut their attempts to intimidate the parent down.
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