In case you need the Police Clearance Certificate, you can request a notice from the Estonian Criminal Records Database.
In case you have an ID-card (with pin-codes and an ID-card reader) it is possible to apply for it online: www.e-toimik.ee.
Nimekast nr 1563
The certificate is in Estonian language and in case you order it yourself it will be issued for free.
You can apply for a consul’s statement in English from the Embassy. In order to do so please make an appointment with the consul in advance by phone +31 (0)703029050, and bring your original certificate of good conduct (in Estonian), a copy of your passport or ID-card and the state fee of €20 (can be paid by card). Please contact the embassy if you would like to apply for the consul’s statement by post.