Generally, players shouldn't be asking to make rolls, they should be interacting with the world and you as GM should be asking for rolls when appropriate to see what the outcome of that interaction is. When it comes to knowledge rolls, that means that when they encounter something new, you should ask them to make the appropriate roll to see what it is. Since a scarecrow is a construct, when they first encounter it, you should ask for an Intelligence (arcana) check to see what they know.
GM: The seemingly harmless scarecrow in the field you were passing suddenly jumps to life. Make an Intelligence (arcana) roll.
PC: I got a 13
GM: This seems to be a construct so you guess it will have most normal construct immunities including mind affecting and poison.
If all you players fail their check to know about the monster, they may be able to get an insight check after interacting with it.
PC: I slash it with my poisoned dagger doing 3 + 6 poison damage.
GM: Ok you slice at its arm causing some of the hay to come out of its arm. Roll an insight check.
PC: I got a 15
GM: Normally when you use this poison you see the wound change color fill with puss, but the straw in this creature's arm doesn't seem to react any differently than if you had sliced him without the poison.
In other words, if you think the characters might have information or insights the players don't have, ask for a roll, or if it is obvious enough, just tell them.
It may even be appropriate when a player tries to do something the character may know if a bad idea to have them roll for the information (or even just tell them) and ask if they still want to do it. Remember the characters are living in this world full time and their lives depend on remembering information about the monsters. Your players usually only do this for a few hours a week as recreation. Reminding them of things the should know is fine sometimes.
PC: I poison my dagger to attack the scarecrow
GM: Ok, you can do that, but remember when we fought scarecrows a few months ago? You tried using poison then and it didn't seem to affect them. Do you still want to try?
Of course don't go overboard with this; you aren't trying to play their characters for them. If they want to do something stupid they should be allowed to, but if their character would know it is stupid, they player should have that information too. The goal here is to try and ensure the player and the character are working with the same information.