Yes, you have to provide proof of qualification. According to the Ministry of Interior:

Documents proving the professional qualifications for performance of the desired job, if this condition follows from the nature of the employment or an international agreement sets such a condition, particularly:

 

• a document proving the required education (such as a diploma); in justified cases, particularly if reasonable doubt exists as to whether you have the required education or whether your education is appropriate for the nature of employment, you will be obliged, at the request of an administrative authority, to prove and submit a document certifying that your foreign education has been recognised by the relevant authority of the CR,

 
• a document proving the required professional qualifications, if such qualifications are required according to other legal regulations (for example, a fork-lift truck operator licence or the appropriate driving license for a tram/bus driver, etc.),

 
• a document proving that you meet the requirements for performing an occupation referred to as “regulated occupation”, if your application concerns this kind of occupation; if you do not already hold such a document, you must apply to the relevant recognition authority of the CR for recognition of your professional qualifications, after filing the application for an employee card. Issuance of the employee card is contingent on your submission of an affirmative decision of the recognition authority

Usually only non-qualified jobs (e.g. construction workers) are exempted.

Yes, you have to provide proof of qualification. According to the Ministry of Interior:

Documents proving the professional qualifications for performance of the desired job, if this condition follows from the nature of the employment or an international agreement sets such a condition, particularly:

• a document proving the required education (such as a diploma); in justified cases, particularly if reasonable doubt exists as to whether you have the required education or whether your education is appropriate for the nature of employment, you will be obliged, at the request of an administrative authority, to prove and submit a document certifying that your foreign education has been recognised by the relevant authority of the CR,

• a document proving the required professional qualifications, if such qualifications are required according to other legal regulations (for example, a fork-lift truck operator licence or the appropriate driving license for a tram/bus driver, etc.),

• a document proving that you meet the requirements for performing an occupation referred to as “regulated occupation”, if your application concerns this kind of occupation; if you do not already hold such a document, you must apply to the relevant recognition authority of the CR for recognition of your professional qualifications, after filing the application for an employee card. Issuance of the employee card is contingent on your submission of an affirmative decision of the recognition authority

Usually only non-qualified jobs (e.g. construction workers) are exempted.